Toeplitz matrices and operators
- Responsibility
- Nikolaï Nikolski ; translated by Danièle Gibbons, Greg Gibbons
- Uniform Title
- Matrices et opérateurs de Toeplitz. English
- Language
- English. In English, translated from the original French
- Publication
- Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2020
- Copyright notice
- ©2020
- Physical description
- xxii, 430 pages : illustrations ; 24 cm
- Series
- Cambridge studies in advanced mathematics ; 182.
At the library
Science Library (Li and Ma)
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| Call number | Status |
|---|---|
| QA188 .N5513 2020 |
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Description
Creators/Contributors
- Author/Creator
- Nikolʹskiĭ, N. K. (Nikolaĭ Kapitonovich), author.
- Contributor
- Gibbons, Danièle, translator.
- Gibbons, Greg, translator.
Contents/Summary
- Bibliography
- Includes bibliographical references and index
- Contents
-
- 1. Why Toeplitz-Hankel? Motivations and panorama--
- 2. Hankel and Toeplitz - brother operators on the space H2--
- 3. H2 theory of Toeplitz operators--
- 4. Applications: Riemann-Hilbert, Wiener-Hopf, singular integral operators (SIO)--
- 5. Toeplitz matrices: moments, spectra, asymptotics-- Appendix A. Key notions of Banach spaces-- Appendix B. Key notions of Hilbert spaces-- Appendix C. An overview of Banach algebras-- Appendix D. Linear operators-- Appendix E. Fredholm operators and the Noether index-- Appendix F. A brief overview of Hardy spaces-- References-- Notation-- Index.
- (source: Nielsen Book Data)
- Summary
-
The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded- and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others. This friendly introduction to Toeplitz theory covers the classical spectral theory of Toeplitz forms and Wiener-Hopf integral operators and their manifestations throughout modern functional analysis. Numerous solved exercises illustrate the results of the main text and introduce subsidiary topics, including recent developments. Each chapter ends with a survey of the present state of the theory, making this a valuable work for the beginning graduate student and established researcher alike. With biographies of the principal creators of the theory and historical context also woven into the text, this book is a complete source on Toeplitz theory.
(source: Nielsen Book Data)
Subjects
Bibliographic information
- Publication date
- 2020
- Copyright date
- 2020
- Series
- Cambridge studies in advanced mathematics ; 182
- Note
- Originally published as: Matrices et opérateurs de Toeplitz by Calvage et Mounet, 2017
- ISBN
- 9781107198500 hardcover
- 110719850X hardcover
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