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arxiv: 1407.1293 · v2 · submitted 2014-07-04 · 🧮 math.CA · math.NA

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

Philippe Jaming (IMB) , Abderrazek Karoui , Ron Kerman , Susanna Spektor
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classification 🧮 math.CA math.NA
keywords hermitealmostapproximationbandexpansionfunctionslimitedtime
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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.

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  1. Convergence theory for Hermite approximations under adaptive coordinate transformations

    math.NA 2026-04 unverdicted novelty 6.0

    Hermite approximations composed with adaptive transformations are equivalent to standard Hermite approximation of the pullback function, yielding error bounds controlled by the regularity of that pullback and enabling...