Wiener's lemma:localization and various approaches

作     者：SHIN Chang Eon SUN Qi-yu 

作者机构：Department of Mathematics Sogang UniversitySeoul 121-742 Korea Department of Mathematics University of Central FloridaOrlando FL 32816 USA 

出 版 物：《Applied Mathematics(A Journal of Chinese Universities)》 (高校应用数学学报（英文版）（B辑）)

年 卷 期：2013年第28卷第4期

页      面：465-484页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by Basic Science Research Program through the National Research Foundation of Korea(NRF) funded by the Ministry of Education,Science and Technology(2013R1A1A2005402) National Science Foundation(DMS-1109063) 

主　　题：Wiener’s lemma infinite matrix stability Wiener algebra Beurling algebra off-diagonal decay inverse closedness 

摘      要：Matrices and integral operators with off-diagonal decay appear in numerous areas of mathematics including numerical analysis and harmonic analysis, and they also play impor-tant roles in engineering science including signal processing and communication engineering. Wiener’s lemma states that the localization of matrices and integral operators are preserved un-der 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.