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Constructive Methods of Wiener-Hopf Factorization

  • Editors
  • I. Gohberg
  • M. A. Kaashoek

Part of the OT 21: Operator Theory: Advances and Applications book series (OT, volume 21)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Canonical and Minimal Factorization

    1. I. Gohberg, M. A. Kaashoek
      Pages 1-7
    2. Joseph A. Ball, André C. M. Ran
      Pages 9-38
    3. H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 39-74
    4. I. Gohberg, M. A. Kaashoek, L. Lerer, L. Rodman
      Pages 75-126
  3. Non-Canonical Wiener-Hopf Factorization

    1. I. Gohberg, M. A. Kaashoek
      Pages 231-233
    2. H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 235-316
    3. H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 317-355
    4. H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 357-372

About this book

Introduction

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.

Keywords

Eigenvalue matrices matrix

Bibliographic information