| 1. |
- Aleman, Alexandru, et al.
(författare)
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The Smirnov class for spaces with the complete Pick property
- 2017
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 96:1, s. 228-242
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Tidskriftsartikel (refereegranskat)abstract
- We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoğlu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails.
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| 2. |
- Balkanova, Olga, et al.
(författare)
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Bounds for a spectral exponential sum
- 2019
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Ingår i: Journal of the London Mathematical Society-Second Series. - : Wiley. - 0024-6107 .- 1469-7750. ; 99:2, s. 249-272
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Tidskriftsartikel (refereegranskat)abstract
- We prove new upper bounds for a spectral exponential sum by refining the process by which one evaluates mean values of L-functions multiplied by an oscillating function. In particular, we introduce a method which is capable of taking into consideration the oscillatory behaviour of the function. This gives an improvement of the result of Luo and Sarnak when T > X1/6+2 theta/3+epsilon. Furthermore, this proves the conjecture of Petridis and Risager in some ranges. Finally, this allows obtaining a new proof of the Soundararajan-Young error estimate in the prime geodesic theorem.
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| 3. |
- Bénéteau, Catherine, et al.
(författare)
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Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94:3, s. 726-746
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Tidskriftsartikel (refereegranskat)abstract
- We study connections between orthogonal polynomials, reproducing kernel functions, and polynomials p minimizing Dirichlet-type norms vertical bar pf-1 vertical bar for a given function f. For [0,1] (which includes the Hardy and Dirichlet spaces of the disk) and general f, we show that such extremal polynomials are non-vanishing in the closed unit disk. For negative, the weighted Bergman space case, the extremal polynomials are non-vanishing on a disk of strictly smaller radius, and zeros can move inside the unit disk. We also explain how dist D(1,fPn), where Pn is the space of polynomials of degree at most n, can be expressed in terms of quantities associated with orthogonal polynomials and kernels, and we discuss methods for computing the quantities in question.
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| 4. |
- Bergh, Daniel
(författare)
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Motivic classes of some classifying stacks
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 93:1, s. 219-243
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Tidskriftsartikel (refereegranskat)abstract
- We prove that the class of the classifying stack BPGL(n) is the multiplicative inverse of the class of the projective linear group PGL(n) in the Grothendieck ring of stacks K-0(Stack(k)) for n = 2 and n = 3 under mild conditions on the base field k. In particular, although it is known that the multiplicativity relation {T} = {S} . {PGL(n)} does not hold for all PGL(n)-torsors T -> S, it holds for the universal PGL(n)-torsors for said n.
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| 5. |
- Björklund, Johan, 1982-
(författare)
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Legendrian contact homology in the product of a punctured Riemann surface and the real line
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94:3, s. 970-992
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Tidskriftsartikel (refereegranskat)abstract
- We give a combinatorial description of the Legendrian differential graded algebra associated to a Legendrian knot in PxR, where P is a punctured Riemann surface. As an application we show that for any integer k and any homology class h in H_1(PxR) there are k Legendrian knots all representing h which are pairwise smoothly isotopic through a formal Legendrian isotopy but which lie in mutually distinct Legendrian isotopy classes.
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| 6. |
- Björn, Anders
(författare)
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Properties of removable singularities for hardy spaces of analytic functions
- 2002
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Ingår i: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 66:3, s. 651-670
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Tidskriftsartikel (refereegranskat)abstract
- Removable singularities for Hardy spaces Hp(O) = {f ? Hol(O) :fp = u in O for some harmonic u}, 0 < p < 8 are studied. A set E ? O is a weakly removable singularity for Hp(O\E) if Hp(O\E) ? Hol(O), and a strongly removable singularity for Hp(O\E) if Hp(O\E) = Hp(O). The two types of singularities coincide for compact E, and weak removability is independent of the domain O. The paper looks at differences between weak and strong removability, the domain dependence of strong removability, and when removability is preserved under unions. In particular, a domain O and a set E ? O that is weakly removable for all Hp, but not strongly removable for any Hp(O\E), 0 < p < 8, are found. It is easy to show that if E is weakly removable for Hp(O\E) and q > p, then E is also weakly removable for Hq(O\E). It is shown that the corresponding implication for strong removability holds if and only if q/p is an integer. Finally, the theory of Hardy space capacities is extended, and a comparison is made with the similar situation for weighted Bergman spaces.
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| 7. |
- Björn, Anders, et al.
(författare)
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The tusk condition and Petrovskii criterion for the normalized p-parabolic equation
- 2019
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Ingår i: Journal of the London Mathematical Society. - : WILEY. - 0024-6107 .- 1469-7750. ; 100:2, s. 623-643
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Tidskriftsartikel (refereegranskat)abstract
- We study boundary regularity for the normalized p-parabolic equation in arbitrary bounded domains. Effros and Kazdan (Indiana Univ. Math. J. 20 (1970) 683-693) showed that the so-called tusk condition guarantees regularity for the heat equation. We generalize this result to the normalized p-parabolic equation, and also obtain Holder continuity. The tusk condition is a parabolic version of the exterior cone condition. We also obtain a sharp Petrovskii criterion for the regularity of the latest moment of a domain. This criterion implies that the regularity of a boundary point is affected if one side of the equation is multiplied by a constant.
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| 8. |
- Björner, Anders., et al.
(författare)
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Subspace arrangements defined by products of linear forms
- 2005
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 71, s. 273-288
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Tidskriftsartikel (refereegranskat)abstract
- The vanishing ideal of an arrangement of linear subspaces in a vector space is considered, and the paper investigates when this ideal can be generated by products of linear forms. A combinatorial construction (blocker duality) is introduced which yields such generators in cases with a great deal of combinatorial structure, and examples are presented that inspired the work. A construction is given which produces all elements of this type in the vanishing ideal of the arrangement. This leads to an algorithm for deciding if the ideal is generated by products of linear forms. Generic arrangements of points in P-2 and lines in P-3 are also considered.
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| 9. |
- Blandigneres, Alain, et al.
(författare)
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Reverse Carleson embeddings for model spaces
- 2013
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 88, s. 437-464
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Tidskriftsartikel (refereegranskat)abstract
- The classical embedding theorem of Carleson deals with finite positive Borel measures mu on the closed unit disk for which there exists a positive constant c such that parallel to f parallel to(L2(mu)) <= c parallel to f parallel to(H2) for all f is an element of H-2, the Hardy space of the unit disk. Lelevre et al. examined measures mu for which there exists a positive constant c such that parallel to f parallel to(L2(mu)) >= c parallel to f parallel to(H2) for all f is an element of H-2. The first type of inequality above was explored with H-2 replaced by one of the model spaces (Theta H-2)(perpendicular to) by Aleksandrov, Baranov, Cohn, Treil, and Vol'berg. In this paper, we discuss the second type of inequality in (Theta H-2)(perpendicular to).
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| 10. |
- Boij, Mats, et al.
(författare)
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Graded betti numbers of Cohen-Macaulay modules and the multiplicity conjecture
- 2008
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 78:1, s. 85-106
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Tidskriftsartikel (refereegranskat)abstract
- We give conjectures on the possible graded Betti numbers of Cohen-Macaulay modules up to multiplication by positive rational numbers. The idea is that the Betti diagrams should be nonh negative linear combinations of pure diagrams. The conjectures are verified in the cases where the structure of resolutions is known, that is: for modules of codimension two, for Glorenstein algebras of codimension three and for complete intersections. The motivation for proposing the conjectures comes from the Multiplicity conjecture of Herzog, Huneke and Srinivasan.
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| 11. |
- Booker, Andrew R., et al.
(författare)
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Twist-minimal trace formulas and the Selberg eigenvalue conjecture
- 2020
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 102:3, s. 1067-1134
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Tidskriftsartikel (refereegranskat)abstract
- We derive a fully explicit version of the Selberg trace formula for twist‐minimal Maass forms of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two theorems. First, conditional on Artin's conjecture, we classify the even 2‐dimensional Artin representations of small conductor; in particular, we show that the even icosahedral representation of smallest conductor is the one found by Doud and Moore (J. Number Theory 118 (2006) 62–70) of conductor 1951. Second, we verify the Selberg eigenvalue conjecture for groups of small level, improving on a result of Huxley (Elementary and analytic theory of numbers, Banach Center Publications 17 (PWN, Warsaw, 1985) 217–306) from 1985.
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| 12. |
- Brubaker, Ben, et al.
(författare)
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Iwahori-metaplectic duality
- 2024
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 109:6
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Tidskriftsartikel (refereegranskat)abstract
- We construct a family of solvable lattice models whose partition functions include p-adic Whittaker functions for general linear groups from two very different sources: from Iwahori-fixed vectors and from metaplectic covers. Interpolating between them by Drinfeld twisting, we uncover unexpected relationships between Iwahori and metaplectic Whittaker functions. This leads to new Demazure operator recurrence relations for spherical metaplectic Whittaker functions. In prior work of the authors it was shown that the row transfer matrices of certain lattice models for spherical metaplectic Whittaker functions could be represented as ‘half-vertex operators’ operating on the q-Fock space of Kashiwara, Miwa and Stern. In this paper the same is shown for all the members of this more general family of lattice models including the one representing Iwahori Whittaker functions.
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| 13. |
- Chacholski, Wojciech, et al.
(författare)
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The A-complexity of a space
- 2002
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Ingår i: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 65, s. 204-222
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Tidskriftsartikel (refereegranskat)abstract
- Suppose that A is a pointed CW-complex. The paper looks at how difficult it is to construct an A-cellular space B from copies of A by repeatedly taking homotopy colimits, this is determined by an ordinal number called the complexity of B. Studying the complexity leads to an iterative technique, based on resolutions, for constructing the A-cellular approximation CWA(X) of an arbitrary space X.
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| 14. |
- Charlier, Christophe, et al.
(författare)
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Airy and Painleve asymptotics for the mKdV equation
- 2019
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750.
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Tidskriftsartikel (refereegranskat)abstract
- We consider the higher order asymptotics for the modified Korteweg-de Vries equation in the Painleve sector. We first show that the solution admits a uniform expansion to all orders in powers of t-1/3 with coefficients that are smooth functions of x(3t)-1/3. We then consider the special case when the reflection coefficient vanishes at the origin. In this case, the leading coefficient which satisfies the Painleve II equation vanishes. We show that the leading asymptotics are instead described by the derivative of the Airy function. We are also able to express the subleading term explicitly in terms of the Airy function.
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| 15. |
- Cordero, Elena, et al.
(författare)
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Schrodinger-type propagators, pseudodifferential operators and modulation spaces
- 2013
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Ingår i: Journal of the London Mathematical Society. - London : London Mathematical Society. - 0024-6107 .- 1469-7750. ; 88, s. 375-395
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Tidskriftsartikel (refereegranskat)abstract
- We prove continuity results for Fourier integral operators with symbols in modulation spaces, acting between modulation spaces. The phase functions belong to a class of non-degenerate generalized quadratic forms that includes Schrödinger propagators and pseudodifferential operators. As a byproduct, we obtain a characterization of all exponents p, q, r1, r2, t1, t2∈[1, ∞] of modulation spaces such that a symbol in Mp, q(ℝ2d) gives a pseudodifferential operator that is continuous from Mr1,r2(ℝd) into Mt1,t2(ℝd).
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| 16. |
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| 17. |
- Englis, M., et al.
(författare)
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Hankel operators and the Dixmier trace on the Hardy space
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94, s. 337-356
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Tidskriftsartikel (refereegranskat)abstract
- We give criteria for the membership of Hankel operators on the Hardy space on the disc in the Dixmier class, and establish estimates for their Dixmier trace. In contrast to the situation in the Bergman space setting, it turns out that there exist Dixmier-class Hankel operators that are not measurable (that is, their Dixmier trace depends on the choice of the underlying Banach limit), as well as Dixmier-class Hankel operators that do not belong to the Schatten-Lorentz ideal. A related question concerning logarithmic interpolation of Besov spaces is also discussed.
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| 18. |
- Falgas-Ravry, Victor, et al.
(författare)
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The codegree threshold of K-4
- 2023
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 107:5, s. 1660-1691
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Tidskriftsartikel (refereegranskat)abstract
- The codegree threshold ex2 (n, F) of a 3-graph F is the minimum d = d(n) such that every 3-graph on n vertices in which every pair of vertices is contained in at least d + 1 edges contains a copy of F as a subgraph. We study ex2 (n, F) when F = K-4 , the 3-graph on 4 vertices with 3 edges. Using flag algebra techniques, we prove that if n is sufficiently large, thenex2 (n, K-4)⩽ (n + 1)/4.This settles in the affirmative a conjecture of Nagle [Congressus Numerantium, 1999, pp. 119-128]. In addition, we obtain a stability result: for every near-extremal configuration G, there is a quasirandom tournament T on the same vertex set such that G is o(n3)-close in the edit distance to the 3-graph C(T) whose edges are the cyclically oriented triangles from T. For infinitely many values of n, we are further able to determine ex2(n, K-4) exactly and to show that tournament-based constructions C(T) are extremal for those values of n.
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| 19. |
- Hall, Jack, et al.
(författare)
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Mayer–Vietoris squares in algebraic geometry
- 2023
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 107:5, s. 1583-1612
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Tidskriftsartikel (refereegranskat)abstract
- We consider various notions of Mayer–Vietoris squares in algebraic geometry. We use these to generalize a number of gluing and push out results of Moret-Bailly, Ferrand–Raynaud, Joyet and Bhatt. An important intermediate step is Gabber's rigidity theorem for henselian pairs, which our methods give a new proof of.
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| 20. |
- Hansen, David, et al.
(författare)
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Perfectoid Shimura varieties and the Calegari–Emerton conjectures
- 2023
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Ingår i: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 108:5, s. 1954-2000
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Tidskriftsartikel (refereegranskat)abstract
- We prove many new cases of a conjecture of Calegari–Emerton describing the qualitative properties of completed cohomology. The heart of our argument is a careful inductive analysis of completed cohomology on the Borel–Serre boundary. As a key input to this induction, we prove a new perfectoidness result for towers of minimally compactified Shimura varieties, generalizing previous work of Scholze.
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| 21. |
- Heckel, Annika, et al.
(författare)
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How does the chromatic number of a random graph vary?
- 2023
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 108:5, s. 1769-1815
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Tidskriftsartikel (refereegranskat)abstract
- The chromatic number & chi;(G)$\chi (G)$ of a graph G$G$ is a fundamental parameter, whose study was originally motivated by applications (& chi;(G)$\chi (G)$ is the minimum number of internally compatible groups the vertices can be divided into, if the edges represent incompatibility). As with other graph parameters, it is also studied from a purely theoretical point of view, and here a key question is: what is its typical value? More precisely, how does & chi;(Gn,1/2)$\chi (G_{n,1/2})$, the chromatic number of a graph chosen uniformly at random from all graphs on n$n$ vertices, behave? This quantity is a random variable, so one can ask (i) for upper and lower bounds on its typical values, and (ii) for bounds on how much it varies: what is the width (for example, standard deviation) of its distribution? On (i) there has been considerable progress over the last 45 years; on (ii), which is our focus here, remarkably little. One would like both upper and lower bounds on the width of the distribution, and ideally a description of the (appropriately scaled) limiting distribution. There is a well-known upper bound of Shamir and Spencer of order n$\sqrt {n}$, improved slightly by Alon to n/logn$\sqrt {n}/\log n$, but no non-trivial lower bound was known until 2019, when the first author proved that the width is at least n1/4-o(1)$n<^>{1/4-o(1)}$ for infinitely many n$n$, answering a longstanding question of Bollobas. In this paper we have two main aims: first, we shall prove a much stronger lower bound on the width. We shall show unconditionally that, for some values of n$n$, the width is at least n1/2-o(1)$n<^>{1/2-o(1)}$, matching the upper bounds up to the error term. Moreover, conditional on a recently announced sharper explicit estimate for the chromatic number, we improve the lower bound to order nloglogn/log3n$\sqrt {n} \log \log n /\log <^>3 n$, within a logarithmic factor of the upper bound. Second, we will describe a number of conjectures as to what the true behaviour of the variation in & chi;(Gn,1/2)$\chi (G_{n,1/2})$ is, and why. The first form of this conjecture arises from recent work of Bollobas, Heckel, Morris, Panagiotou, Riordan and Smith. We will also give much more detailed conjectures, suggesting that the true width, for the worst case n$n$, matches our lower bound up to a constant factor. These conjectures also predict a Gaussian limiting distribution.
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| 22. |
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| 23. |
- Hoffmann-Stenhof, M., et al.
(författare)
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Many-particle hardy inequalities
- 2008
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 77, s. 99-114
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we prove three different types of the so-called many-particle Hardy inequalities. One of them is a 'classical type' which is valid in any dimension d not equal 2. The second type deals with 2-dimensional magnetic Dirichlet forms, where every particle is supplied with a solenoid. Finally we show that Hardy inequalities for fermionic functions (fully anti-symmetric for d = 1, 2) hold true in all dimensions.
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| 24. |
- Isralowitz, Joshua, et al.
(författare)
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Commutators in the two scalar and matrix weighted setting
- 2022
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 106:1, s. 1-26
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we approach the two weighted boundedness of commutators via matrix weights. This approach provides both a sufficient and a necessary condition for the two weighted boundedness of commutators with an arbitrary linear operator in terms of one matrix weighted norm inequalities for this operator. Furthermore, using this approach, we surprisingly provide conditions that almost characterize the two matrix weighted boundedness of commutators with CZOs and completely arbitrary matrix weights, which is even new in the fully scalar one weighted setting. Finally, our method allows us to extend the two weighted Holmes/Lacey/Wick results to the fully matrix setting (two matrix weights and a matrix symbol), completing a line of research initiated by the first two authors.
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| 25. |
- Kelmer, Dubi, et al.
(författare)
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Fourier expansion of light-cone Eisenstein series
- 2023
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 108:6, s. 2175-2247
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Tidskriftsartikel (refereegranskat)abstract
- In this work, we give an explicit formula for the Fourier coefficients of Eisenstein series corresponding to certain arithmetic lattices acting on hyperbolic n + 1 -space. As a consequence, we obtain results on location of all poles of these Eisenstein series aswell as their supremumnorms. We use this information to get new results on counting rational points on spheres.
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| 26. |
- Lang, Jan, et al.
(författare)
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Essential norms and localization moduli of Sobolev embeddings for general domains
- 2008
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 78:2, s. 373-391
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Tidskriftsartikel (refereegranskat)abstract
- We introduce new measures of non-compactness for the embedding operator Ep,q(Ω):Lp1(Ω)→Lq(Ω) and describe their relations with the essential norm of Ep, q(Ω), 'local' isoperimetric and isocapacitary constants. An explicit formula for the essential norm of Ep, q(Ω) is obtained for domains with a power cusp on the boundary and bounded C1 domains. The Neumann problem for a particular Schrödinger operator is discussed on domains with a power cusp.
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| 27. |
- Lang, Lionel
(författare)
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Amoebas of curves and the Lyashko-Looijenga map
- 2019
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Ingår i: Journal of the London Mathematical Society. - : London Mathematical Society. - 0024-6107 .- 1469-7750. ; 100:1, s. 301-322
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Tidskriftsartikel (refereegranskat)abstract
- For any curve V in a toric surface X, we study the critical locus S subset of V of the moment map mu from V to its compactified amoeba mu(V). For any complete linear system |L| given by an ample line bundle L on X, we show that the critical locus S subset of V is smooth as long as the curve V is outside of a subset of real codimension 1 in |L|. In particular, the complement of the latter subset appears to be disconnected for general L. It suggests a classification problem analogous to Hilbert's Sixteenth Problem, namely the topological classification of pairs (V,S) for curves V is an element of|L|. The description of the critical locus S in terms of the logarithmic Gau ss map gamma:V -> CP1 relates the latter problem to the study of the Lyashko-Looijenga map (ll). The map ll associates to a generic curve V is an element of|L| the unordered set of the critical values of gamma on CP1. We prove two statements concerning ll that are crucial for our classification problem: the map ll is algebraic; the map ll extends to nodal curves in |L|. This fact allows us to construct many examples of pairs (V,S) by perturbing nodal curves.
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| 28. |
- Liu, Hong, et al.
(författare)
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Stability from graph symmetrisation arguments with applications to inducibility
- 2023
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 108:3, s. 1121-1162
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Tidskriftsartikel (refereegranskat)abstract
- We present a sufficient condition for the stability property of extremal graph problems that can be solved via Zykov's symmetrisation. Our criterion is stated in terms of an analytic limit version of the problem. We show that, for example, it applies to the inducibility problem for an arbitrary complete bipartite graph B, which asks for the maximum number of induced copies of B in an n-vertex graph, and to the inducibility problem for K2,1,1,1 and K3,1,1, the only complete partite graphs on at most five vertices for which the problem was previously open.
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| 29. |
- Lorensen, Karl, et al.
(författare)
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Generating numbers of rings graded by amenable and supramenable groups
- 2024
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 109:1
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Tidskriftsartikel (refereegranskat)abstract
- A ring ? has unbounded generating number (UGN) if,for every positive integer ?, there is no ?-module epimorphism ?? → ??+1. For a ring ? = ⨁g∈? ?g gradedby a group ? such that the base ring ?1 has UGN, weidentify several sets of conditions under which ? mustalso have UGN. The most important of these are: (1)? is amenable, and there is a positive integer ? suchthat, for every g ∈ ?, ?g ≅ (?1)? as ?1-modules for some? = 1, … , ?; (2) ? is supramenable, and there is a positive integer ? such that, for every g ∈ ?, ?g ≅ (?1)? as?1-modules for some ? = 0, … , ?. The pair of conditions(1) leads to three different ring-theoretic characterizations of the property of amenability for groups. We alsoconsider rings that do not have UGN; for such a ring?, the smallest positive integer ? such that there is an?-module epimorphism ?? → ??+1 is called the generating number of ?, denoted gn(?). If ? has UGN, then wedefine gn(?) ∶= ℵ0. We describe several classes of examples of a ring ? graded by an amenable group ? such thatgn(?) ≠ gn(?1).MSC 202016P99, 16S35, 16W50, 20F65, 43A07 (primary), 16D90 (secondary)
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| 30. |
- Malbos, Philippe, et al.
(författare)
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Shuffle polygraphic resolutions for operads
- 2023
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 107:1, s. 61-122
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Tidskriftsartikel (refereegranskat)abstract
- Shuffle operads were introduced to forget the symmetric group actions on symmetric operads while preserving all possible operadic compositions. Rewriting methods were then applied to symmetric operads via shuffle operads: in particular, a notion of Gröbner basis was introduced for shuffle operads with respect to a total order on tree monomials. In this article, we introduce the structure of shuffle polygraphs as a categorical model for rewriting in shuffle operads, which generalizes the Gröbner bases approach by removing the constraint of a monomial order for the orientation of the rewriting rules. We define (Formula presented.) -operads as internal (Formula presented.) -categories in the category of shuffle operads. We show how to extend a convergent shuffle polygraph into a shuffle polygraphic resolution generated by the overlapping branchings of the original polygraph. Finally, we prove that a shuffle operad presented by a quadratic convergent shuffle polygraph is Koszul.
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| 31. |
- Maligranda, Lech
(författare)
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Weighted inequalities for quasi-monotone functions
- 1998
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Ingår i: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 57:2, s. 363-370
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Tidskriftsartikel (refereegranskat)abstract
- The purpose of this paper is to give characterizations of weights for which reverse inequalities of the Hölder type for quasi-monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement the results of Bergh-Burenov-Persson (1994), Heinig-Maligranda (1995), Heinig-Stepanov (1993) and Stepanov (1993, 1994) for the values of parameters p and q with 1[less-than-or-eq, slant]p[less-than-or-eq, slant]q<[infty infinity].
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| 32. |
- Nordqvist, Jonas, et al.
(författare)
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Residue fixed point index and wildly ramified power series
- 2020
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Ingår i: Journal of the London Mathematical Society. - : John Wiley & Sons. - 0024-6107 .- 1469-7750. ; 102:2, s. 470-497
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we study power series having a fixed point of multiplier 1. First, we give a closed formula for the residue fixed point index, in terms of the first coefficients of the power series. Then, we use this formula to study wildly ramified power series in positive characteristic. Among power series having a multiple fixed point of small multiplicity, we characterize those having the smallest possible lower ramification numbers in terms of the residue fixed point index. Furthermore, we show that these power series form a generic set, and, in the case of convergent power series, we also give an optimal lower bound for the distance to other periodic points.
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| 33. |
- Rodriguez-Lopez, Salvador
(författare)
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A homomorphism theorem for bilinear multipliers
- 2013
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 88:2, s. 619-639
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we prove an abstract homomorphism theorem for bilinear multipliers in the setting of locally compact Abelian (LCA) groups. We also provide some applications. In particular, we obtain a bilinear abstract version of de Leeuw's theorem for bilinear multipliers of strong and weak types. We also obtain necessary conditions on bilinear multipliers on non-compact LCA groups, yielding boundedness for the corresponding operators on products of rearrangement invariant spaces. Our investigations extend some existing results in ℝn to the framework of general LCA groups, and yield new boundedness results for bilinear multipliers in quasi-Banach spaces.
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| 34. |
- Roos, Jan-Erik
(författare)
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Derived functors of inverse limits revisited
- 2006
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Ingår i: Journal of the London Mathematical Society. - 1469-7750 .- 0024-6107. ; 73:1, s. 31-47
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Tidskriftsartikel (refereegranskat)abstract
- We prove, correct and extend several results of an earlier paper of ours (using and recalling several of our later papers) about the derived functors of projective limit in abelian categories. In particular we prove that if C is an abelian category satisfying the Grothendieck axioms AB3 and AB4* and having a set of generators then the first derived functor of projective limit vanishes on so-called Mittag-Leffler sequences in C. The recent examples given by Deligne and Neeman show that the condition that the category has a set of generators is necessary. The condition AB4* is also necessary, and indeed we give for each integer $m \geq 1$ an example of a Grothendieck category Cm and a Mittag-Leffler sequence in Cm for which the derived functors of its projective limit vanish in all positive degrees except m. This leads to a systematic study of derived functors of infinite products in Grothendieck categories. Several explicit examples of the applications of these functors are also studied.
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| 35. |
- Rydh, David, et al.
(författare)
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An intrinsic construction of the principal component of the Hilbert scheme
- 2010
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 82, s. 459-481
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Tidskriftsartikel (refereegranskat)abstract
- The principal component of the Hilbert scheme of n points on a scheme X is the closure of the open subset parameterizing n distinct points. In this article we construct the principal component as a certain blow-up of the symmetric product of X. Our construction is based on a local explicit analysis of etale families, from which the appropriate universal property, needed to identify the principal component with the blow-up, is derived.
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| 36. |
- Rydhe, Eskil
(författare)
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An Agler-type model theorem for C0-semigroups of Hilbert space contractions
- 2016
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 93:2, s. 420-438
-
Tidskriftsartikel (refereegranskat)abstract
- We investigate suitable conditions for a C0-semigroup (T(t))t≥0 of Hilbert space contractions to be unitarily equivalent to the restriction of the adjoint shift semigroup (S∗γ(t))t≥0 to an invariant subspace of the standard weighted Bergman space Aγ−2(C+,K). It turns out that (T(t))t≥0 admits a model by (S∗γ(t))t≥0 if and only if its cogenerator is γ-hypercontractive and limt→0T(t)=0 in strong operator topology. We then discuss how such semigroups can be characterized without involving the cogenerator. A sufficient condition is that, for each t>0, the operator T(t) is γ-hypercontractive. Surprisingly, this condition is necessary if and only if γ is integer. The paper is concluded with a conjecture that would imply a more symmetric characterization.
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| 37. |
- Salberger, Per, 1957, et al.
(författare)
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Rational points on complete intersections of higher degree, and mean values of Weyl sums
- 2010
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Ingår i: Journal of the London Mathematical Society - Second Series. - : Wiley. - 0024-6107 .- 1469-7750. ; 82, s. 317-342
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Tidskriftsartikel (refereegranskat)abstract
- We establish upper bounds for the number of rational points of bounded height on complete intersections. When the degree of the intersection is sufficiently large in terms of its dimension, and the contribution arising from appropriate linear spaces is removed, these bounds are smaller than those arising from the expectation of 'square-root cancellation'. In particular, there is a paucity of non-diagonal solutions to the equation, provided that d >= (2s)(4s). There are consequences for the approximate distribution function of Weyl sums of higher degree, and also for quasi-diagonal behaviour in mean values of smooth Weyl sums.
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| 38. |
- Shapiro, Boris, 1957-
(författare)
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Algebro-geometric aspects of Heine-Stieltjes theory
- 2011
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 83, s. 36-56
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Tidskriftsartikel (refereegranskat)abstract
- The goal of the paper is to develop a Heine-Stieltjes theory for univariate linear differential operators of higher order. Namely, for a given linear ordinary differential operator d(z) = Pk i=1 Qi(z) di dzi with polynomial coefficients set r = maxi=1,...,k(degQi(z)−i). If d(z) satisfies the conditions: i) r 0 and ii) degQk(z) = k + r we call it a non-degenerate higher Lam´e operator. Following the classical approach of E. Heine and T. Stieltjes, see [18], [41] we study the multiparameter spectral problem of finding all polynomials V (z) of degree at most r such that the equation: d(z)S(z) + V (z)S(z) = 0 has for a given positive integer n a polynomial solution S(z) of degree n. We show that under some mild non-degeneracy assumptions there exist exactly `n+r n ´ such polynomials Vn,i(z) whose corresponding eigenpolynomials Sn,i(z) are of degree n. We generalize a number of well-known results in this area and discuss occurring degeneracies.
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| 39. |
- Skjelnes, Roy Mikael
(författare)
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On the representability of H ilb(n)k x ((x))
- 2000
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Ingår i: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 62, s. 757-770
-
Tidskriftsartikel (refereegranskat)abstract
- Let k[x]((x)) be the polynomial ring k[x] localized in the maximal ideal (x) subset of k[x]. The paper studies the Hilbert functor parametrizing ideals of colength n in this ring having support at the origin. The main result is that this functor is not representable. A complete description of the functor as a limit of representable functors is also given.
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| 40. |
- Strömbergsson, Andreas, 1973-, et al.
(författare)
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An effective equidistribution result for SL(2,R) ∝(R2)⊕k and application to inhomogeneous quadratic forms
- 2020
-
Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 102:1, s. 143-204
-
Tidskriftsartikel (refereegranskat)abstract
- Let G=SL(2,R) (sic) (R-2)(circle plus k) and let Gamma be a congruence subgroup of SL(2,Z) (sic) (Z(2))(circle plus k). We prove a polynomially effective asymptotic equidistribution result for special types of unipotent orbits in Gamma\G which project to pieces of closed horocycles in SL(2,Z)\SL(2,R). As an application, we prove an effective quantitative Oppenheim-type result for the quadratic form (m(1)-alpha)(2)+(m(2)-beta)(2)-(m(3)-alpha)(2)-(m(4)-beta)(2), for (alpha,beta)is an element of R-2 of Diophantine type, following the approach by Marklof [Ann. of Math. 158 (2003) 419-471] using theta sums.
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| 41. |
- Södergren, Anders
(författare)
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On the distribution of angles between the N shortest vectors in a random lattice
- 2011
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 84:3, s. 749-764
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Tidskriftsartikel (refereegranskat)abstract
- We determine the joint distribution of the lengths of, and angles between, the N shortest lattice vectors in a random n-dimensional lattice as n→∞. Moreover, we interpret the result in terms of eigenvalues and eigenfunctions of the Laplacian on flat tori. Finally, we discuss the limit distribution of any finite number of successive minima of a random n-dimensional lattice as n→∞.
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| 42. |
- Xantcha, Qimh Richey
(författare)
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Gabriel 2-quivers for finitary 2-categories
- 2015
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 92, s. 615-632
-
Tidskriftsartikel (refereegranskat)abstract
- We develop the theory of 2-quivers and quiver 2-categories to run in parallel with the classical theory of quiver algebras. A quiver 2-category is always finitary, and, conversely, every finitary 2-category will be bi-equivalent with a quiver 2-category for a unique underlying reduced 2-quiver. As an application, we produce an example of a fiat 2-category, one of whose Duflo involutions is not self-adjoint.
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| 43. |
- Andersson, Erik
(författare)
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A uniqueness theorem in the inverse spectral theory of a certain higher-order ordinary differential equation using Paley-Wiener methods
- 2005
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Ingår i: Journal of the London Mathematical Society. - 0024-6107. ; 72:1, s. 169-184
-
Tidskriftsartikel (refereegranskat)abstract
- The paper examines a higher-order ordinary differential equation of the form P[u]:= Sigma(j,k=0)(m) D(j)a(jk)D(k)u = gimel u, x is an element of [0, b), where D=i(d/dx), and where the coefficients a(jk), j, k is an element of [0,M], with a = 1, satisfy certain regularity conditions and are chosen so that the matrix (a(jk)) is hermitean. It is also assumed that m > 1. More precisely, it is proved, using Paley-Wiener methods, that the corresponding spectral measure determines the equation up to conjugation by a function of modulus 1. The paper also discusses under which additional conditions the spectral measure uniquely determines the coefficients a(jk), j, k E [0, m], J + k not equal 2m, as well as b and the boundary conditions at 0 and at b (if any).
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| 44. |
- Bennewitz, Christer, et al.
(författare)
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Approximation numbers of Sobolev embedding operators on an interval
- 2004
-
Ingår i: Journal of the London Mathematical Society. - 0024-6107. ; 70, s. 244-260
-
Tidskriftsartikel (refereegranskat)abstract
- Consider the Sobolev embedding operator from the space of functions in W-1,W-p(I) with average zero into L-p, where I is a finite interval and p > 1. This operator plays an important role in recent work. The operator norm and its approximation numbers in closed form are calculated. The closed form of the norm and approximation numbers of several similar Sobolev embedding operators on a finite interval have recently been found. It is proved in the paper that most of these operator norms and approximation numbers on a finite interval are the same.
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| 45. |
- Ekström, Fredrik, et al.
(författare)
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Hausdorff dimension of random limsup sets
- 2018
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107. ; 98:3, s. 661-686
-
Tidskriftsartikel (refereegranskat)abstract
- We prove bounds for the almost sure value of the Hausdorff dimension of the limsup set of a sequence of balls in Rd whose centres are independent, identically distributed random variables. The formulas obtained involve the rate of decrease of the radii of the balls and multifractal properties of the measure according to which the balls are distributed, and generalise formulas that are known to hold for particular classes of measures.
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| 46. |
- Essen, M, et al.
(författare)
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Repulsive fixpoints of analytic functions with applications to complex dynamics
- 2000
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Ingår i: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES. - : LONDON MATH SOC. - 0024-6107. ; 62, s. 139-148
-
Tidskriftsartikel (refereegranskat)abstract
- Let G be a family of functions analytic in a domain D in the complex plane. It is proved that G is a normal family, provided that for each f epsilon G, there exists k = k(f) > 1 such that the kth iterate f(k) has no repulsive fixpoint in D. A new proof of
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| 47. |
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| 48. |
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| 49. |
- Svensson, Martin
(författare)
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Holomorphic foliations, harmonic morphisms and the Walczak formula
- 2003
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Ingår i: Journal of the London Mathematical Society. - 0024-6107. ; 68:3, s. 781-794
-
Tidskriftsartikel (refereegranskat)abstract
- A formula of Walczak is applied to two situations in differential geometry. Holomorphic distributions on Kahler manifolds are studied, and it is shown how the formula simplifies to a Bochner type formula, which is particularly useful in the study of integrable distributions. Then the Walczak formula is applied in the context of harmonic morphisms, where it provides a means of investigating the vertical Laplacian of the dilation. It is shown that, under some additional conditions on the map and the domain, the p-energy is infinite for p sufficiently large.
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| 50. |
- Viola, Joseph Anthony
(författare)
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Resolvent estimates for non-selfadjoint operators with double characteristics
- 2012
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Ingår i: Journal of the London Mathematical Society. - : Wiley. - 0024-6107. ; 85, s. 41-78
-
Tidskriftsartikel (refereegranskat)abstract
- We study resolvent estimates for non-selfadjoint semiclassical pseudodifferential operators with double characteristics. Assuming that the quadratic approximation along the double characteristics is elliptic, we obtain polynomial upper bounds on the resolvent in a suitable region inside the pseudospectrum.
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