Title
Wiener's lemma: localization and various approaches
Abbreviated Journal Title
Appl. Math.-J. Chin. Univ. Ser. B
Keywords
Wiener's lemma; infinite matrix; stability; Wiener algebra; Beurling; algebra; off-diagonal decay; inverse closedness; FINITE SECTION METHOD; OFF-DIAGONAL DECAY; INTEGRAL-OPERATORS; INFINITE; MATRICES; BANACH-ALGEBRAS; INVERSE-CLOSEDNESS; SPECTRUM; SPACES; RECONSTRUCTION; SUBALGEBRAS; Mathematics, Applied
Abstract
Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play important roles in engineering science including signal processing and communication engineering. Wiener's lemma states that the localization of matrices and integral operators are preserved under inversion. In this introductory note, we re-examine several approaches to Wiener's lemma for matrices. We also review briefly some recent advances on localization preservation of operations including nonlinear inversion, matrix factorization and optimization.
Journal Title
Applied Mathematics-a Journal of Chinese Universities Series B
Volume
28
Issue/Number
4
Publication Date
1-1-2013
Document Type
Article
Language
English
First Page
465
Last Page
484
WOS Identifier
ISSN
1005-1031
Recommended Citation
"Wiener's lemma: localization and various approaches" (2013). Faculty Bibliography 2010s. 4694.
https://stars.library.ucf.edu/facultybib2010/4694
Comments
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