Wiener's lemma: localization and various approaches
Abbreviated Journal Title
Appl. Math.-J. Chin. Univ. Ser. B
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
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.
Applied Mathematics-a Journal of Chinese Universities Series B
"Wiener's lemma: localization and various approaches" (2013). Faculty Bibliography 2010s. 4694.