Sampling and \(\Pi\)-sampling expansions
type: Item
instance of: scholarly article
title: Sampling and \(\Pi\)-sampling expansions
zbMATH Open document ID: 0996.94020
DOI: 10.1007/BF02829533
author: R. Smith
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 2001-03-27T00:00:00Z
review text: Using the hyperfinite representation of functions and generalized functions, this paper develops a rigorous version of the so-called ``delta method'' approach to sampling theory. (For a derivation of the delta method using standard analysis, see \textit{M. Z. Nashed} and \textit{G. G. Walter} [Math. Control Signals Syst. 4, 363-390 (1991; Zbl 0734.46019)].) The nonstandard analysis approach adopted by the paper under review yields a slightly more general version of the classical WKS sampling theorem for band-limited functions.
Mathematics Subject Classification ID: 94C10
Mathematics Subject Classification ID: 42C99
zbMATH DE Number: 1553301
zbMATH Keywords: sampling expansions
zbMATH Keywords: WKS sampling theorem
zbMATH Keywords: nonstandard analysis
zbMATH Keywords: hyperfinite sums
reviewed by: Richard A. Zalik
MaRDI profile type: Publication
cites work: General sampling theorems for functions in reproducing kernel Hilbert spaces
cites work: Hyperfinite representation of distributions
full work available at URL: https://doi.org/10.1007/bf02829533
OpenAlex ID: W1982323299
description: scientific article; zbMATH DE number 1553301