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TitleConstructive Methods of Wiener-Hopf Factorization [electronic resource] / edited by I. Gohberg, M. A. Kaashoek
ImprintBasel : Birkhรคuser Basel, 1986
Connect tohttp://dx.doi.org/10.1007/978-3-0348-7418-2
Descript XII, 410 p. online resource

SUMMARY

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 โ{128}ข. . . โ{128}ข 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 . โ{128}ข [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 rยท J J J J J where Aj is a square matrix of size nj x nโ{128}ข say. B and C are j j j matrices of sizes n. x m and m x n . โ{128}ข 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


CONTENT

I: Canonical and Minimal Factorization -- Editorial introduction -- Left Versus Right Canonical Factorization -- Wiener-Hopf Equations With Symbols Analytic In A Strip -- On Toeplitz and Wiener-Hopf Operators with Contour-Wise Rational Matrix and Operator Symbols -- Canonical Pseudo-Spectral Factorization and Wiener-Hopf Integral Equations -- Minimal Factorization of Integral operators and Cascade Decompositions of Systems -- II: Non-Canonical Wiener-Hopf Factorization -- Editorial introduction -- Explicit Wiener-Hopf Factorization and Realization -- Invariants for Wiener-Hopf Equivalence of Analytic Operator Functions -- Multiplication by Diagonals and Reduction to Canonical Factorization -- Symmetric Wiener-Hopf Factorization of Self-Adjoint Rational Matrix Functions and Realization


Mathematics Mathematical analysis Analysis (Mathematics) Mathematics Analysis



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