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Constructive Methods of Wiener-Hopf Factorization

  • Book
  • © 1986

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Editors:
  1. I. Gohberg
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    You can also search for this editor in PubMed   Google Scholar

  2. M. A. Kaashoek
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Part of the book series: Operator Theory: Advances and Applications (OT, volume 21)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XII
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  2. Canonical and Minimal Factorization

    1. Editorial Introduction

      • I. Gohberg, M. A. Kaashoek
      Pages 1-7

    2. Left Versus Right Canonical Wiener-Hopf Factorization

      • Joseph A. Ball, André C. M. Ran
      Pages 9-38

    3. Wiener-Hopf Equations with Symbols Analytic in A Strip

      • H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 39-74

    4. On Toeplitz and Wiener-Hopf Operators with Contourwise Rational Matrix and Operator Symbols

      • I. Gohberg, M. A. Kaashoek, L. Lerer, L. Rodman
      Pages 75-126

    5. Canonical Pseudo-Spectral Factorization and Wiener-Hopf Integral Equations

      • Leen Roozemond
      Pages 127-156

    6. Minimal Factorization of Integral Operators and Cascade Decompositions of Systems

      • I. Gohberg, M. A. Kaashoek
      Pages 157-230

  3. Non-Canonical Wiener-Hopf Factorization

    1. Editorial Introduction

      • I. Gohberg, M. A. Kaashoek
      Pages 231-233

    2. Explicit Wiener-Hopf Factorization and Realization

      • H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 235-316

    3. Invariants for Wiener-Hopf Equivalence of Analytic Operator Functions

      • H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 317-355

    4. Multiplication by Diagonals and Reduction to Canonical Factorization

      • H. Bart, I. Gohberg, M. A. Kaashoek
      Pages 357-372

    5. Symmetric Wiener-Hopf Factorization of Selfadjoint Rational Matrix Functions and Realization

      • M. A. Kaashoek, A. C. M. Ran
      Pages 373-409
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Constructive Methods of Wiener-Hopf Factorization

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

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-7418-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1986

  • Softcover ISBN: 978-3-0348-7420-5Published: 19 April 2012

  • eBook ISBN: 978-3-0348-7418-2Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XII, 410

  • Topics: Analysis

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