Decomposition of spaces of distributions induced by Hermite expansions

2007/05/02 by Pencho Petrushev, Yuan Xu, Petrushev, Pencho +1
Economics, Econometrics and Finance · Mathematics · #42B35 #42C15 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0705.0318

openalex publication_date 2007/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Decomposition systems with rapidly decaying elements (needlets) based on Hermite functions are introduced and explored. It is proved that the Triebel-Lizorkin and Besov spaces on \R^d induced by Hermite expansions can be characterized in terms of the needlet coefficients. It is also shown that the Hermite Triebel-Lizorkin and Besov spaces are, in general, different from the respective classical spaces.

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