Banach frames for multivariate alpha-modulation spaces

Lasse Borup; Morten Nielsen

doi:doi:10.1016/j.jmaa.2005.08.091

Banach frames for multivariate alpha-modulation spaces

Lasse Borup, Morten Nielsen

Department of Mathematical Sciences

Research output: Contribution to journal › Journal article › Research › peer-review

34 Citations (Scopus)

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.

Original language	English
Journal	Journal of Mathematical Analysis and Applications
Volume	321
Issue number	2
Pages (from-to)	880-895
Number of pages	16
ISSN	0022-247X
DOIs	https://doi.org/doi:10.1016/j.jmaa.2005.08.091
Publication status	Published - 2006

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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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AU - Nielsen, Morten

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AB - 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.

U2 - doi:10.1016/j.jmaa.2005.08.091

DO - doi:10.1016/j.jmaa.2005.08.091

M3 - Journal article

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VL - 321

SP - 880

EP - 895

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Banach frames for multivariate alpha-modulation spaces

Abstract

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