Title

Wiener's lemma for infinite matrices

Authors

Authors

Q. Y. Sun

Comments

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Abbreviated Journal Title

Trans. Am. Math. Soc.

Keywords

Wiener's lemma; Banach algebra; inverse of infinite matrices; HOMOGENEOUS TYPE; FRAMES; SPACES; LOCALIZATION; SYMMETRY; ALGEBRAS; Mathematics

Abstract

The classical Wiener lemma and its various generalizations are important and have numerous applications in numerical analysis, wavelet theory, frame theory, and sampling theory. There are many different equivalent formulations for the classical Wiener lemma, with an equivalent formulation suitable for our generalization involving commutative algebra of infinite matrices W := {(a(j-j'))(j,j'is an element of Zd) : Sigma(j is an element of Zd) |a(j)| < infinity}. In the study of spline approximation, (diffusion) wavelets and a. ne frames, Gabor frames on non-uniform grid, and non-uniform sampling and reconstruction, the associated algebras of infinite matrices are extremely non-commutative, but we expect those non-commutative algebras to have a similar property to Wiener's lemma for the commutative algebra W. In this paper, we consider two non-commutative algebras of infinite matrices, the Schur class and the Sjostrand class, and establish Wiener's lemmas for those matrix algebras.

Journal Title

Transactions of the American Mathematical Society

Volume

359

Issue/Number

7

Publication Date

1-1-2007

Document Type

Article

Language

English

First Page

3099

Last Page

3123

WOS Identifier

WOS:000245149100006

ISSN

0002-9947

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