Title

Wiener'S Lemma: Localization And Various Approaches

Keywords

Beurling algebra; infinite matrix; inverse closedness; off-diagonal decay; stability; Wiener algebra; Wiener's lemma

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. © 2013 Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag Berlin Heidelberg.

Publication Date

12-1-2013

Publication Title

Applied Mathematics

Volume

28

Issue

4

Number of Pages

465-484

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s11766-013-3215-6

Socpus ID

84890507723 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84890507723

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