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Titlebook: Constructive Methods of Wiener-Hopf Factorization; I. Gohberg,M. A. Kaashoek Book 1986 Birkh?user Verlag Basel 1986 Eigenvalue.matrices.ma

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書(shū)目名稱Constructive Methods of Wiener-Hopf Factorization
編輯I. Gohberg,M. A. Kaashoek
視頻videohttp://file.papertrans.cn/237/236111/236111.mp4
叢書(shū)名稱Operator Theory: Advances and Applications
圖書(shū)封面Titlebook: Constructive Methods of Wiener-Hopf Factorization; I. Gohberg,M. A. Kaashoek Book 1986 Birkh?user Verlag Basel 1986 Eigenvalue.matrices.ma
描述The main part of this paper concerns Toeplitz operators of which the symbol W is an m x m matrix function defined on a disconnected curve r. The curve r is assumed to be the union of s + 1 nonintersecting simple smooth closed contours rOo r ?. . . ? rs which form the positively l oriented boundary of a finitely connected bounded domain in t. Our main requirement on the symbol W is that on each contour rj the function W is the restriction of a rational matrix function Wj which does not have poles and zeros on rj and at infinity. Using the realization theorem from system theory (see. e. g . ? [1]. Chapter 2) the rational matrix function Wj (which differs from contour to contour) may be written in the form 1 (0. 1) W . (A) = I + C. (A - A. f B. A E r· J J J J J where Aj is a square matrix of size nj x n? say. B and C are j j j matrices of sizes n. x m and m x n . ? respectively. and the matrices A. J x J J and Aj = Aj - BjC have no eigenvalues on r . (In (0. 1) the functions j j Wj are normalized to I at infinity.
出版日期Book 1986
關(guān)鍵詞Eigenvalue; matrices; matrix
版次1
doihttps://doi.org/10.1007/978-3-0348-7418-2
isbn_softcover978-3-0348-7420-5
isbn_ebook978-3-0348-7418-2Series ISSN 0255-0156 Series E-ISSN 2296-4878
issn_series 0255-0156
copyrightBirkh?user Verlag Basel 1986
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On Toeplitz and Wiener-Hopf Operators with Contourwise Rational Matrix and Operator Symbols operators with symbols defined on a curve composed of several non-intersecting simple closed contours. Also criteria and explicit formulas for canonical factorization of matrix functions relative to a compound contour are presented. The matrix functions we work with are rational on each of the comp
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Canonical Pseudo-Spectral Factorization and Wiener-Hopf Integral Equationstorization is introduced, and all possible factorizations of this type are described in terms of realizations of the symbol and certain supporting projections. With each canonical pseudo-spectral factorization is related a pseudo-resolvent kernel, which satisfies the resolvent identities and is used
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https://doi.org/10.1007/978-3-642-02460-3y matrix. A . of W relative to the real line is a multiplicative decomposition: . in which the factors W. and W. are of the form . where k. and k. are m × m matrix functions with entries in L. (-∞,0] and L.[0, ∞), respectively, and
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On Toeplitz and Wiener-Hopf Operators with Contourwise Rational Matrix and Operator Symbols results are stated in terms of invertibility properties of a certain finite matrix called indicator, which is built from the realizations. The analysis does not depend on finite dimensionality and is carried out for operator valued symbols.
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