| 1. |
- Aleman, Alexandru, et al.
(author)
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The Smirnov class for spaces with the complete Pick property
- 2017
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 96:1, s. 228-242
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Journal article (peer-reviewed)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.
(author)
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Bounds for a spectral exponential sum
- 2019
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In: Journal of the London Mathematical Society-Second Series. - : Wiley. - 0024-6107 .- 1469-7750. ; 99:2, s. 249-272
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Journal article (peer-reviewed)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.
(author)
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Orthogonal polynomials, reproducing kernels, and zeros of optimal approximants
- 2016
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94:3, s. 726-746
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Journal article (peer-reviewed)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
(author)
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Motivic classes of some classifying stacks
- 2016
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 93:1, s. 219-243
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Journal article (peer-reviewed)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-
(author)
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Legendrian contact homology in the product of a punctured Riemann surface and the real line
- 2016
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 94:3, s. 970-992
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Journal article (peer-reviewed)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
(author)
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Properties of removable singularities for hardy spaces of analytic functions
- 2002
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In: Journal of the London Mathematical Society. - 0024-6107 .- 1469-7750. ; 66:3, s. 651-670
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Journal article (peer-reviewed)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.
(author)
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The tusk condition and Petrovskii criterion for the normalized p-parabolic equation
- 2019
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In: Journal of the London Mathematical Society. - : WILEY. - 0024-6107 .- 1469-7750. ; 100:2, s. 623-643
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Journal article (peer-reviewed)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.
(author)
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Subspace arrangements defined by products of linear forms
- 2005
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 71, s. 273-288
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Journal article (peer-reviewed)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.
(author)
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Reverse Carleson embeddings for model spaces
- 2013
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 88, s. 437-464
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Journal article (peer-reviewed)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.
(author)
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Graded betti numbers of Cohen-Macaulay modules and the multiplicity conjecture
- 2008
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In: Journal of the London Mathematical Society. - : Wiley. - 0024-6107 .- 1469-7750. ; 78:1, s. 85-106
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Journal article (peer-reviewed)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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