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Analysis of Toeplitz Operators

  • Book
  • © 1990

Overview

Authors:
  1. Albrecht Böttcher

    1. Sektion Mathematik, Wissenschaftsbereich Analysis, Technische Universität Chemnitz, Chemnitz, Germany

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  2. Bernd Silbermann

    1. Sektion Mathematik, Wissenschaftsbereich Analysis, Technische Universität Chemnitz, Chemnitz, Germany

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  • First systematical and at the same time the most comprehensive presentation of the large body of knowledge one has gained for Toeplitz operators, including many techniques and results that are due to the authors themselves
  • Addressed to graduate students who are approaching the subject for the first time and to specialist in operator theory, but it will also be of interest to numerical analysts, physicists, and statisticians

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (10 chapters)

  1. Front Matter

    Pages 1-11
    Download chapter PDF

  2. Auxiliary material

    • Albrecht Böttcher, Bernd Silbermann
    Pages 13-46

  3. Basic theory

    • Albrecht Böttcher, Bernd Silbermann
    Pages 47-100

  4. Symbol analysis

    • Albrecht Böttcher, Bernd Silbermann
    Pages 101-151

  5. Toeplitz operators on H2

    • Albrecht Böttcher, Bernd Silbermann
    Pages 152-215

  6. Toeplitz operators on Hp

    • Albrecht Böttcher, Bernd Silbermann
    Pages 216-247

  7. Toeplitz operators on lp

    • Albrecht Böttcher, Bernd Silbermann
    Pages 248-276

  8. Finite Section Method

    • Albrecht Böttcher, Bernd Silbermann
    Pages 277-338

  9. Toeplitz operators over the quarter-plane

    • Albrecht Böttcher, Bernd Silbermann
    Pages 339-396

  10. Wiener-Hopf integral operators

    • Albrecht Böttcher, Bernd Silbermann
    Pages 397-428

  11. Toeplitz determinants

    • Albrecht Böttcher, Bernd Silbermann
    Pages 429-486

  12. Back Matter

    Pages 487-512
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Keywords

About this book

This book was originally intended as an extended version of our book "Invertibility and Asymptotics of Toeplitz Matrices", which appeared in 1983. We planned to discuss several topics in more detail, but our main concern was to incorporate a whole series of new results obtained during the last few years. However, we soon realized that the program we had in mind required new thoughts from both the methodological and substantial point of view, and so we decided to attempt writing a completely new book on the analysis of Toeplitz operators. There are at least two reasons for the continuous and increasing interest in Toeplitz operators. On the one hand, Toeplitz operators are of importance in connection with a variety of problems in physics, probability theory, information and control theory, and several other fields. Although we shall not embark on these problems, the selection of the material of this book is to a certain extent determined by such applications. On the other hand, besidesthe differential operators, Toeplitz operators constitute one of the most important classes of non-selfadjoint operators and they are a fascinating example of the fruitful interplay between such topics as operator theory, function theory, and the theory of Banach algebras. One main purpose of this book is to elucidate some of the ideas and methods illustrating just the latter aspect.

Reviews

From the reviews of the second edition:

"The first edition of this book was published in 1990 and became a standard reference … . The area of mathematics that includes the analysis of Toeplitz operators has been particularly active over the last two decades and the authors of this book have been actively taking part in this development. … new material was incorporated with recent developments in topics … . this new edition is certainly welcome and will find a wide audience." (Amarino Lebre, Zentralblatt MATH, Vol. 1098 (24), 2006)

"This edition, like the first, is a clear, detailed, and self-contained development of the field. The scope of this book is immense. It is 661 pages long. … For those of us that work in the area of Toeplitz operators, and for those who only occasionally think about Toeplitz operators, this book is an invaluable resource. We are grateful that we have a complete, elegant, and current account of an interesting and intriguing subject."(Estelle L. Basor, Mathematical Reviews, Issue 2007 k)

Authors and Affiliations

  • Sektion Mathematik, Wissenschaftsbereich Analysis, Technische Universität Chemnitz, Chemnitz, Germany

    Albrecht Böttcher, Bernd Silbermann

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