Decomposition of spaces of distributions induced by Hermite expansions

Details Decomposition of spaces of distributions induced by Hermite expansions Decomposition of spaces of distributions induced by Hermite expansions

2007-05-02

arxiv.org/abs/0705.0318v1

Mathematics

Classical Analysis and ODEs

34 pages

Scientific paper

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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