Banach frames for multivariate alpha-modulation spaces

Lasse Borup, Morten Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review

21 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 languageEnglish
JournalJournal of Mathematical Analysis and Applications
Volume321
Issue number2
Pages (from-to)880-895
Number of pages16
ISSN0022-247X
DOIs
Publication statusPublished - 2006

Fingerprint

Banach Frames
Modulation Spaces
Modulation
Besov Spaces
Tensor Product
Univariate
Tensors
Simplify
Union
Term

Cite this

@article{ca856f90fdfc11dbad54000ea68e967b,
title = "Banach frames for multivariate alpha-modulation spaces",
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.",
author = "Lasse Borup and Morten Nielsen",
year = "2006",
doi = "doi:10.1016/j.jmaa.2005.08.091",
language = "English",
volume = "321",
pages = "880--895",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press",
number = "2",

}

Banach frames for multivariate alpha-modulation spaces. / Borup, Lasse; Nielsen, Morten.

In: Journal of Mathematical Analysis and Applications, Vol. 321, No. 2, 2006, p. 880-895.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Banach frames for multivariate alpha-modulation spaces

AU - Borup, Lasse

AU - Nielsen, Morten

PY - 2006

Y1 - 2006

N2 - 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.

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

VL - 321

SP - 880

EP - 895

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -