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

2014/07/04 by Jaming, Philippe, Karoui, Abderrazek, Kerman, Ron +1
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1407.1293

Abstract

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 L²-Sobolev space with fixed compact support.

Related

• Hermite expansions for spaces of functions with nearly optimal time-frequency decay
• Approximation in Hermite spaces of smooth functions
• Scaling Optimized Hermite Approximation Methods
• Local approximation using Hermite functions
• Hermite expansions of C₀-groups and cosine functions