Constructive Methods of Wiener-Hopf Factorization

Kaashoek

ISBN 10: 3034874200 / ISBN 13: 9783034874205

Published by Birkhäuser Basel, Birkhäuser Basel Apr 2012, 2012

About this Item

This item is printed on demand - Print on Demand Titel. Neuware -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.Springer Basel AG in Springer Science + Business Media, Heidelberger Platz 3, 14197 Berlin 424 pp. Englisch.

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Bibliographic Details

• Title: Constructive Methods of Wiener-Hopf Factorization
• Publisher: Birkhäuser Basel, Birkhäuser Basel Apr 2012
• Publication Date: 2012
• Language: English
• ISBN 10: 3034874200
• ISBN 13: 9783034874205
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 244W x 170H x 23D millimeters 244 millimeters width by 170 millimeters height by 23 millimeters depth
• Weight: 728 grams

About this title

Synopsis

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.