THE APPROXIMATION OF ALMOST TIME AND BAND LIMITED FUNCTIONS BY THEIR EXPANSION IN SOME ORTHOGONAL POLYNOMIALS BASES

Philippe Jaming (1) , Abderrazek Karoui (2) , Susanna Spektor (3)

1 IMB - Institut de Mathématiques de Bordeaux
2 Département de mathématiques
3 University of Alberta

The aim of this paper is to investigate the quality of approximation of almost time and almost band-limited functions by its expansion in three classical orthogonal polynomials bases: the Hermite, Legendre and Chebyshev bases. As a corollary, this allows us to obtain the quality of approximation in the L 2 −Sobolev space by these orthogonal polynomials bases. Also, we obtain the rate of the Legendre series expansion of the prolate spheroidal wave functions. Some numerical examples are given to illustrate the different results of this work.

Domaines: Analyse classique [math.CA]; Analyse numérique [math.NA]; Traitement du signal et de l'image [eess.SP]

Philippe Jaming, Abderrazek Karoui, Susanna Spektor. THE APPROXIMATION OF ALMOST TIME AND BAND LIMITED FUNCTIONS BY THEIR EXPANSION IN SOME ORTHOGONAL POLYNOMIALS BASES. Journal of Approximation Theory, 2016, 212, pp.41-65. ⟨hal-01103588⟩