Approximation of almost time and band limited functions I: Hermite expansions

Philippe Jaming (1) , Abderrazek Karoui (2) , Ron Kerman (3) , Susanna Spektor (4)

1 IMB - Institut de Mathématiques de Bordeaux
2 Département de mathématiques
3 Department of Mathematics & Statistics
4 University of Alberta

This paper is not meant for publication. It is an expended and more detailed version of part of the paper "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 band limited functions by its expansion in the Hermite and scaled Hermite basis. As a corollary, this allows us to obtain the rate of convergence of the Hermite expansion of function in the $L^2$-Sobolev space with fixed compact support.

Mots clés: Almost time and band limited functions; Hermite functions

Domaines: Analyse classique [math.CA]; Analyse numérique [math.NA]

Philippe Jaming, Abderrazek Karoui, Ron Kerman, Susanna Spektor. Approximation of almost time and band limited functions I: Hermite expansions: Preliminary version of the paper "The approximation of almost time and band limited functions by their expansion in some orthogonal polynomials bases". [Intern report] imb. 2014. ⟨hal-01018357v2⟩