Preliminary version of the paper "The approximation of almost time and band limited functions by theirexpansion in some orthogonal polynomials bases"

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 theirexpansion 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