The approximation of almost time- and band-limited functions by their expansion in some orthogonal polynomials bases

The aim of this paper is to investigate the quality of approximation of almost time- and almost band-limited functions by its expansion in two classical orthogonal polynomials bases: the Hermite basis and the ultraspherical polynomials bases (which include Legendre and Chebyshev bases as particular...

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Bibliographic Details
Published in:Journal of approximation theory 2016-12, Vol.212, p.41-65
Main Authors: Jaming, Philippe, Karoui, Abderrazek, Spektor, Susanna
Format: Article
Language:English
Subjects:
Almost time and band limited functions
Chebyshev polynomials
Classical Analysis and ODEs
Engineering Sciences
Hermite functions
Legendre polynomials
Mathematics
Numerical Analysis
Prolate spheroidal wave functions
Signal and Image processing
Ultraspherical polynomials
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Summary:The aim of this paper is to investigate the quality of approximation of almost time- and almost band-limited functions by its expansion in two classical orthogonal polynomials bases: the Hermite basis and the ultraspherical polynomials bases (which include Legendre and Chebyshev bases as particular cases). As a corollary, this allows us to obtain the quality of approximation in the L2-Sobolev space by these orthogonal polynomials bases. Also, we obtain the rate of convergence of the Legendre series expansion of the prolate spheroidal wave functions.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2016.08.002