Chromatic series with prolate spheroidal wave functions
type: Item
instance of: scholarly article
title: Chromatic series with prolate spheroidal wave functions
zbMATH Open document ID: 1180.41028
DOI: 10.1216/JIE-2008-20-2-263
published in: Journal of Integral Equations and Applications
publication date: 2008-08-05T00:00:00Z
review text: Ignjatovic introduced the theory of chromatic derivatives in the technical report of the Kromos Corporation. Chromatic series are series expansions in which the coefficients are linear combinations of derivatives of a function. They were introduced as a replacement for Taylor's series and are based on orthogonal polynomials. Prolate spheroidal wave functions (PSWFs) arise as solution of an integral equation. This makes them band limited functions in a Paley-Wiener space, but because they are also solutions to a Sturm-Liouville problem, they behave very much like polynomials locally. Since the PSWFs are close to orthogonal polynomials they can be used to replace them in the Ignjatovic theory. It has been extended further to prolate spheroidal wavelet series that then combine chromatic series with sampling series. This leads to an over determined system which can use either local or global data to approximate the original function.
reviewed by: C. L. Parihar
Mathematics Subject Classification ID: 41A58
Mathematics Subject Classification ID: 41A30
Mathematics Subject Classification ID: 42A38
zbMATH DE Number: 5306884
zbMATH Keywords: chromatic derivatives
zbMATH Keywords: prolate spheroidal wave functions
zbMATH Keywords: wavelets
zbMATH Keywords: signal processing
author: Gilbert G. Walter
MaRDI profile type: Publication
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full work available at URL: jie-2008-20-2-263
OpenAlex ID: W1967359041
description: scientific article; zbMATH DE number 5306884