Hilbert spaces of distributions having an orthogonal basis of exponentials
type: Item
instance of: scholarly article
title: Hilbert spaces of distributions having an orthogonal basis of exponentials
zbMATH Open document ID: 0960.42010
DOI: 10.1007/BF02511156
author: Jean-Pierre Gabardo
published in: The Journal of Fourier Analysis and Applications
publication date: 2001-05-01T00:00:00Z
full work available at URL: https://eudml.org/doc/59643
review text: One of the main results is a characterization of the Hilbert spaces consisting of distributions supported on \([0,1]\), for which \(\{e^{2\pi i mx}\}_{m\in \mathbb Z}\) is a complete orthonormal system. The results are generalized to spectral pairs, and used to generalize Shannon's sampling theorem.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 94C10
zbMATH DE Number: 1445612
zbMATH Keywords: band-limited
zbMATH Keywords: sampling
zbMATH Keywords: spectral pairs
MaRDI profile type: Publication
cites work: Sampling Theorem for the Fourier Transform of a Distribution with Bounded Support
cites work: Q4861331
cites work: Commuting self-adjoint partial differential operators and a group theoretic problem
cites work: Nonuniform multiresolution analyses and spectral pairs
cites work: Q4381496
cites work: On the distributional Fourier duality and its applications
cites work: Spectral theory of finite volume domains in \(R^ n\).
cites work: Harmonic analysis on tori
cites work: Spectral theory for Borel sets in \(\mathbb{R}{}^ n\) of finite measure
cites work: Group theoretic and geometric properties of multivariable Fourier series
cites work: Characterization of bandlimited functions and processes
cites work: Spectral theory of commuting self-adjoint partial differential operators
cites work: Spectral sets whose spectrum is a lattice with a base
cites work: Sampling series for band-limited generalized functions
cites work: Band-limited functions and the sampling theorem
cites work: Q4319646
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description: scientific article; zbMATH DE number 1445612