An Introduction to Operator Polynomials

✍ Scribed by Prof. Leiba Rodman (auth.)

• Publisher: Birkhäuser Basel
• Year: 1989
• Tongue: English
• Leaves: 400
• Series: Operator Theory: Advances and Applications 38
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-7
Linearizations....Pages 8-38
Representations and Divisors of Monic Operator Polynomials....Pages 39-92
Vandermonde Operators and Common Multiples....Pages 93-129
Stable Factorizations of Monic Operator Polynomials....Pages 130-177
Self-Adjoint Operator Polynomials....Pages 178-223
Spectral Triples and Divisibility of Non-Monic Operator Polynomials....Pages 224-268
Polynomials with Given Spectral Pairs and Exactly Controllable Systems....Pages 269-296
Common Divisors and Common Multiples....Pages 297-316
Resultant and Bezoutian Operators....Pages 317-360
Wiener-Hopf Factorization....Pages 361-370
Back Matter....Pages 371-391

✦ Subjects

Science, general