Trigonometric bases for matrix weighted Lp-spaces

Morten Nielsen

doi:10.1016/j.jmaa.2010.06.015

Trigonometric bases for matrix weighted L_p-spaces

Morten Nielsen

Department of Mathematical Sciences

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

3 Citations (Scopus)

Abstract

We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space L_p(T;W). Then trigonometric quasi-greedy bases for L_p(T;W) are considered. Quasi-greedy bases are systems for which the simple thresholding approximation algorithm converges in norm. It is proved that such a trigonometric basis can be quasi-greedy only for p=2, and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.

Original language	English
Journal	Journal of Mathematical Analysis and Applications
Volume	371
Issue number	2
Pages (from-to)	784-792
Number of pages	9
ISSN	0022-247X
DOIs	https://doi.org/10.1016/j.jmaa.2010.06.015
Publication status	Published - 2010

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title = "Trigonometric bases for matrix weighted Lp-spaces",

abstract = "We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space Lp(T;W). Then trigonometric quasi-greedy bases for Lp(T;W) are considered. Quasi-greedy bases are systems for which the simple thresholding approximation algorithm converges in norm. It is proved that such a trigonometric basis can be quasi-greedy only for p=2, and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.",

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PY - 2010

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AB - We give a complete characterization of 2π-periodic matrix weights W for which the vector-valued trigonometric system forms a Schauder basis for the matrix weighted space Lp(T;W). Then trigonometric quasi-greedy bases for Lp(T;W) are considered. Quasi-greedy bases are systems for which the simple thresholding approximation algorithm converges in norm. It is proved that such a trigonometric basis can be quasi-greedy only for p=2, and whenever the system forms a quasi-greedy basis, the basis must actually be a Riesz basis.

U2 - 10.1016/j.jmaa.2010.06.015

DO - 10.1016/j.jmaa.2010.06.015

M3 - Journal article

SN - 0022-247X

VL - 371

SP - 784

EP - 792

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -