Banach frames for multivariate alpha-modulation spaces

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Abstract

The α-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Riesz sequences based on tensor products of univariate brushlet functions, which simplifies the analysis of the full frame. We show that the multivariate α-modulation spaces can be completely characterized by the Banach frames constructed.

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The α-modulation spaces [$Mathematical Term$], form a family of spaces that include the Besov and modulation spaces as special cases. This paper is concerned with construction of Banach frames for α-modulation spaces in the multivariate setting. The frames constructed are unions of independent Riesz sequences based on tensor products of univariate brushlet functions, which simplifies the analysis of the full frame. We show that the multivariate α-modulation spaces can be completely characterized by the Banach frames constructed.

Original languageEnglish
JournalJournal of Mathematical Analysis and Applications
Volume321
Issue number2
Pages (from-to)880-895
Number of pages16
ISSN0022-247X
DOI
Publication statusPublished - 2006
Publication categoryResearch
Peer-reviewedYes
ID: 9147199