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Interpolation of Rational Matrix Functions

  • Book
  • © 1990

Overview

Authors:
  1. Joseph A. Ball

    1. Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

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  2. Israel Gohberg

    1. School of Mathematical Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat Aviv, Tel-Aviv, Israel

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  3. Leiba Rodman

    1. Department of Mathematics, The College of William and Mary, Williamsburg, USA

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 45)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Introduction

    1. Introduction

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 1-4

  3. Homogeneous Interpolation Problems with Standard Data

    1. Front Matter

      Pages 5-6
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    2. Null Structure for Analytic Matrix Functions

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 7-39

    3. Null Structure and Interpolation Problems for Matrix Polynomials

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 40-64

    4. Local Data for Meromorphic Matrix Functions

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 65-85

    5. Rational Matrix Functions

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 86-133

    6. Rational Matrix Functions with Null and Pole Structure at Infinity

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 134-161

    7. Rational Matrix Functions with J-Unitary Values on the Imaginary Line

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 162-177

    8. Rational Matrix Functions with J-Unitary Values on the Unit Circle

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 178-198

  4. Back Matter

    Pages 199-200
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  5. Homogeneous Interpolation Problems with Other Forms of Local Data

    1. Front Matter

      Pages 201-201
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    2. Interpolation Problems with Null and Pole Pairs

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 202-208

    3. Interpolation Problems for Rational Matrix Functions Based on Divisibility

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 209-212

    4. Polynomial Interpolation Problems Based on Divisibility

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 213-223

    5. Coprime Representation and an Interpolation Problem

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 224-234

  6. Back Matter

    Pages 235-235
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  7. Subspace Interpolation Problems

    1. Front Matter

      Pages 236-236
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    2. Null-Pole Subspaces: Elementary Properties

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 237-267

    3. Null-Pole Subspace for Matrix Functions with J-Unitary Values on the Imaginary Axis or Unit Circle

      • Joseph A. Ball, Israel Gohberg, Leiba Rodman
      Pages 268-279
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Keywords

About this book

This book aims to present the theory of interpolation for rational matrix functions as a recently matured independent mathematical subject with its own problems, methods and applications. The authors decided to start working on this book during the regional CBMS conference in Lincoln, Nebraska organized by F. Gilfeather and D. Larson. The principal lecturer, J. William Helton, presented ten lectures on operator and systems theory and the interplay between them. The conference was very stimulating and helped us to decide that the time was ripe for a book on interpolation for matrix valued functions (both rational and non-rational). When the work started and the first partial draft of the book was ready it became clear that the topic is vast and that the rational case by itself with its applications is already enough material for an interesting book. In the process of writing the book, methods for the rational case were developed and refined. As a result we are now able to present the rational case as an independent theory. After two years a major part of the first draft was prepared. Then a long period of revising the original draft and introducing recently acquired results and methods followed. There followed a period of polishing and of 25 chapters and the appendix commuting at various times somewhere between Williamsburg, Blacksburg, Tel Aviv, College Park and Amsterdam (sometimes with one or two of the authors).

Authors and Affiliations

  • Department of Mathematics, Virginia Polytechnic Institute and State University, Blacksburg, USA

    Joseph A. Ball

  • School of Mathematical Science, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel-Aviv University, Ramat Aviv, Tel-Aviv, Israel

    Israel Gohberg

  • Department of Mathematics, The College of William and Mary, Williamsburg, USA

    Leiba Rodman

Bibliographic Information

  • Book Title: Interpolation of Rational Matrix Functions

  • Authors: Joseph A. Ball, Israel Gohberg, Leiba Rodman

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-7709-1

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1990

  • Hardcover ISBN: 978-3-7643-2476-6Due: 01 July 1990

  • Softcover ISBN: 978-3-0348-7711-4Published: 03 October 2013

  • eBook ISBN: 978-3-0348-7709-1Published: 11 November 2013

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIII, 605

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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