Nikolai Nikolski

Toeplitz Matrices and Operators (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 2. Januar 2020
• Englisch
• ISBN-13: 9781108187572
• Artikelnr.: 62736810

Autorenporträt

Nikolaï Nikolski is Professor Emeritus at the Université de Bordeaux, working primarily in analysis and operator theory. He has been co-editor of four international journals, editor of more than fifteen books, and published numerous articles and research monographs. He has also supervised twenty-six Ph.D. students, including three Salem Prize winners. Professor Nikolski was elected Fellow of the American Mathematical Society (AMS) in 2013 and received the Prix Ampère of the French Academy of Sciences in 2010.

Inhaltsangabe

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.