Wiener's lemma: localization and various approaches

    Authors

    C. E. Shin;Q. Y. Sun

    Comments

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    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

    WOS:000328347600007

    ISSN

    1005-1031

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