Spectral gaps for sets and measures

DOI10.1007/s11511-012-0076-4zbMath1245.42008arXiv0908.2079OpenAlexW2027236268MaRDI QIDQ414340

Alexei G. Poltoratski

Publication date: 11 May 2012

Published in: Acta Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0908.2079

zbMATH Keywords

Toeplitz operatorsspectral gapsBeurling-Malliavin theoryuncertainty principle in harmonic analysis

Mathematics Subject Classification ID

Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Measures on groups and semigroups, etc. (43A05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38)

Related Items (19)

Gap and Type problems in Fourier analysis ⋮ Crystalline temperate distributions with uniformly discrete support and spectrum ⋮ Inner Functions, Completeness and Spectra ⋮ Restricted interpolation by meromorphic inner functions ⋮ Spectra of Cantor measures ⋮ A problem on completeness of exponentials ⋮ Gap problem for separated sequences and Beurling-Malliavin theorem ⋮ Bernstein’s Problem on Weighted Polynomial Approximation ⋮ Type alternative for Frostman measures ⋮ On the determinacy problem for measures ⋮ A generalization of the first Beurling-Malliavin theorem ⋮ Weighted exponential approximation and non-classical orthogonal spectral measures ⋮ Pointwise convergence of the non-linear Fourier transform ⋮ On meromorphic inner functions in the upper half-plane ⋮ Spectrality of the planar Sierpinski family ⋮ Toeplitz order ⋮ Pólya sequences, Toeplitz kernels and gap theorems ⋮ Kernels of Toeplitz operators ⋮ On the multidimensional Nazarov lemma

Cites Work

• Weighted exponential approximation and non-classical orthogonal spectral measures
• Beurling-Malliavin theory for Toeplitz kernels
• Pólya sequences, Toeplitz kernels and gap theorems
• Isometric embeddings of coinvariant subspaces of the shift operator
• On the two-dimensional Coulomb gas
• On Fourier transforms of measures with compact support
• On the closure of characters and the zeros of entire functions
• The support of functions and distributions with a spectral gap.
• Extensions of Hardy spaces and their use in analysis
• The statistical mechanics of the classical two-dimensional Coulomb gas is exactly solved
• Meromorphic Inner Functions, Toeplitz Kernels and the Uncertainty Principle
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