Beurling-Malliavin theory for Toeplitz kernels

By Nikolai G. Makarov, Alexei Poltoratski. 2007

57 citations recorded by the source corpus.

AbstractWe consider the family of Toeplitz operators $T_{J\bar{S}^{a}}$ acting in the Hardy space H2 in the upper halfplane; J and S are given meromorphic inner functions, and a is a real parameter. In the case where the argument of S has a power law type behavior on the real line, we compute the critical value $$c(J,S)=\inf\left\{a:\mathop{\mathrm{ker}}T_{J\bar{S}^{a}}\ne0\right\}.$$ The formula for c(J,S) generalizes the Beurling-Malliavin theorem on the radius of completeness for a system of exponentials.

Subfields: Applied Mathematics

View Paper: https://www.semanticscholar.org/paper/9ab3d31490f1d8e014910b5bda45109103f86c1a

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In Applied Mathematics

1. Mishko Mitkovski
2. A. Baranov
3. Dmitry Yakubovich
4. Alexei Poltoratski

Citations in the corpus

• Uniqueness (2021, unknown): “Probably the best known uniqueness result in the calculus of variations is the following: If I is a strictly convex functional, defined on an open convex subset of a normed space, then it has at most one critical point, which is the global minimum whenever it exists.”
• Polya sequences, Toeplitz kernels and gap theorems (2009, methodology): “s {In} such that #(X ∩ In) |In| → 0 then there exists a non constant zero type entire function that is bounded on X. Ourapproachis similartothe onedevelopedbythe secondauthorandN. Makarov in [15] and [16], where it was used to obtain extensions and applications of the Beurling-Malliavintheory. In pa”
• Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators (2012, result): “ess of systems of reproducing kernels in de Branges spaces and of their biorthogonal systems. New approaches to the study of such problems were recently introduced by Makarov and Poltoratski in [65], [66] and by Baranov, Belov and Borichev in [8], [9], [11], [10]; the results of the present paper bo”