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An Introduction to Operator Polynomials

  • Book
  • © 1989

Overview

Authors:
  1. Leiba Rodman

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

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Part of the book series: Operator Theory: Advances and Applications (OT, volume 38)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xii
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  2. Introduction

    • Leiba Rodman
    Pages 1-7

  3. Linearizations

    • Leiba Rodman
    Pages 8-38

  4. Representations and Divisors of Monic Operator Polynomials

    • Leiba Rodman
    Pages 39-92

  5. Vandermonde Operators and Common Multiples

    • Leiba Rodman
    Pages 93-129

  6. Stable Factorizations of Monic Operator Polynomials

    • Leiba Rodman
    Pages 130-177

  7. Self-Adjoint Operator Polynomials

    • Leiba Rodman
    Pages 178-223

  8. Spectral Triples and Divisibility of Non-Monic Operator Polynomials

    • Leiba Rodman
    Pages 224-268

  9. Polynomials with Given Spectral Pairs and Exactly Controllable Systems

    • Leiba Rodman
    Pages 269-296

  10. Common Divisors and Common Multiples

    • Leiba Rodman
    Pages 297-316

  11. Resultant and Bezoutian Operators

    • Leiba Rodman
    Pages 317-360

  12. Wiener-Hopf Factorization

    • Leiba Rodman
    Pages 361-370

  13. Back Matter

    Pages 371-391
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Keywords

About this book

This book provides an introduction to the modern theory of polynomials whose coefficients are linear bounded operators in a Banach space - operator polynomials. This theory has its roots and applications in partial differential equations, mechanics and linear systems, as well as in modern operator theory and linear algebra. Over the last decade, new advances have been made in the theory of operator polynomials based on the spectral approach. The author, along with other mathematicians, participated in this development, and many of the recent results are reflected in this monograph. It is a pleasure to acknowledge help given to me by many mathematicians. First I would like to thank my teacher and colleague, I. Gohberg, whose guidance has been invaluable. Throughout many years, I have worked wtih several mathematicians on the subject of operator polynomials, and, consequently, their ideas have influenced my view of the subject; these are I. Gohberg, M. A. Kaashoek, L. Lerer, C. V. M. van der Mee, P. Lancaster, K. Clancey, M. Tismenetsky, D. A. Herrero, and A. C. M. Ran. The following mathematicians gave me advice concerning various aspects of the book: I. Gohberg, M. A. Kaashoek, A. C. M. Ran, K. Clancey, J. Rovnyak, H. Langer, P.

Authors and Affiliations

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

    Leiba Rodman

Bibliographic Information

  • Book Title: An Introduction to Operator Polynomials

  • Authors: Leiba Rodman

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-9152-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Birkhäuser Verlag Basel 1989

  • Hardcover ISBN: 978-3-7643-2324-0Due: 01 July 1989

  • Softcover ISBN: 978-3-0348-9928-4Published: 08 October 2011

  • eBook ISBN: 978-3-0348-9152-3Published: 06 December 2012

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XII, 391

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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