Constructive Methods of Wienner-Hopf Factorization (Operator Theory, Advances and Applications)

I. Gohberg; M. A. Kaashoek

ISBN 10: 0817618260 / ISBN 13: 9780817618261

Published by Birkhauser, 1986

About this Item

Solidly bound in green boards with some edge wear; inside are no names or markings;

Seller Inventory # 012150

Bibliographic Details

• Title: Constructive Methods of Wienner-Hopf Factorization (Operator Theory, Advances and Applications)
• Publisher: Birkhauser
• Publication Date: 1986
• Language: English
• ISBN 10: 0817618260
• ISBN 13: 9780817618261
• Binding: Hardcover
• Condition: Very Good
• Seller catalogs:
  • Mathematics

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.