Systems of Reproducing Kernels and their Biorthogonal: Completeness or Incompleteness?

DOI10.1093/imrn/rnq281zbMath1239.46012arXiv1005.1197OpenAlexW2963835903MaRDI QIDQ3104520

Yurii Belov, Anton D. Baranov

Publication date: 14 December 2011

Published in: International Mathematics Research Notices (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.1197

zbMATH Keywords

Riesz basisreproducing kernel Hilbert spacePaley-Wiener spacede Branges spaceexact system

Mathematics Subject Classification ID

Summability and bases; functional analytic aspects of frames in Banach and Hilbert spaces (46B15) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Hilbert spaces of continuous, differentiable or analytic functions (46E20) Representations of entire functions of one complex variable by series and integrals (30D10) Spaces and algebras of analytic functions of one complex variable (30H99) Completeness problems, closure of a system of functions of one complex variable (30B60)

Related Items (11)

Spectral synthesis in Hilbert spaces of entire functions ⋮ Geometric Properties of Reproducing Kernels in Hilbert Spaces of Entire Functions ⋮ Completeness and spectral synthesis of nonselfadjoint one-dimensional perturbations of selfadjoint operators ⋮ Geometry of reproducing kernels in model spaces near the boundary ⋮ Uniqueness of Gabor series ⋮ Systems biorthogonal to exponential systems on a finite union of intervals ⋮ On a characterization of Riesz bases via biorthogonal sequences ⋮ Summability properties of Gabor expansions ⋮ Bessel sequences with finite upper density in de Branges spaces ⋮ Spectral theory of rank one perturbations of normal compact operators ⋮ Spectral synthesis in de Branges spaces

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