Title

A Generalized Sampling Theorem With The Inverse Of An Arbitrary Square Summable Sequence As Sampling Points

Keywords

Cardinal series; Interpolation of entire functions; Kramer sampling theorem; Shannon sampling theorem

Abstract

In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points tn = an + b if n = 0, 1, 2,... and tn = an + c if n = 0, -1, -2,..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, h = 0 = c, the famous Whittaker-Shannon-Kotel 'nikov sampling theorem is obtained as a special case.

Publication Date

12-1-1996

Publication Title

Journal of Fourier Analysis and Applications

Volume

2

Issue

3

Number of Pages

302-314

Document Type

Article

Personal Identifier

scopus

Socpus ID

84951599257 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84951599257

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