Decomposition of Spaces of Distributions Induced by Hermite Expansions |
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| Authors: | Pencho Petrushev Yuan Xu |
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| Institution: | (1) Department of Mathematics, University of South Carolina, Columbia, SC 29208, USA;(2) Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, 1113, Bulgaria;(3) Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA |
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| 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.
The first author has been supported by NSF Grant DMS-0709046 and the second author by NSF Grant DMS-0604056. |
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| Keywords: | Localized kernels Frames Hermite polynomials Triebel-Lizorkin spaces Besov spaces |
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