| 1. |
- 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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| 2. |
- 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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| 3. |
- 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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| 4. |
- 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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| 5. |
- 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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| 6. |
- 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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| 7. |
- 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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| 8. |
- 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
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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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