This article is cited in 1 paper

Analog of the Whittaker–Kotelnikov–Shannon Theorem from the Point of View of Fourier–Bessel Analysis

S. S. Platonov

Petrozavodsk State University

Abstract: In this paper, we obtain an analog of the Whittaker–Kotelnikov–Shannon theorem on the basis of the harmonic Fourier–Bessel analysis. We construct a new interpolation formula for a class of entire functions of exponential type in which generalized Bessel translations are used instead of the usual translations.

Keywords: harmonic analysis, Whittaker–Kotelnikov–Shannon (sampling) theorem, interpolation formula, entire function of exponential type, Bessel function, Hilbert space.

UDC: 517.5

Received: 06.06.2006
Revised: 08.02.2007

DOI: 10.4213/mzm3835

 English version: Mathematical Notes, 2008, 83:2, 238–245

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