Wiener's lemma: localization and various approaches

초록

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.

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