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Toeplitz matrices and operators / Nikolai¯ Nikolski
Material type:
TextLanguage: English Series: Cambridge Studies in Advanced MathematicsPublication details: Cambridge University Press : 2020. CambridgeEdition: 1st edDescription: xxii, 430 p : 22 cmISBN: - 9781107198500
- 512.9434 NIK
Contents:
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.
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,
| Item type | Current library | Collection | Shelving location | Call number | Status | Barcode | |
|---|---|---|---|---|---|---|---|
Reference
|
Kalaignar Centenary Library Madurai | ENGLISH-REFERENCE BOOKS | மூன்றாம் தளம் / Third floor | 512.9434 NIK (Browse shelf(Opens below)) | Not for loan | 285182 |
Includes bibliographical references (p. 395-415), notation and index.
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,
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.