Approximation of almost time and band limited functions I: Hermite expansions
arXiv:1407.12933 citationsh-index: 20
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Provides theoretical convergence guarantees for Hermite expansions of bandlimited functions, which is an incremental contribution to approximation theory.
The paper studies how well almost time and band limited functions can be approximated by Hermite and scaled Hermite expansions, deriving convergence rates for functions in L²-Sobolev spaces with compact support.
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.