Toeplitz Matrices and Operators

A friendly introduction to Toeplitz theory and its applications throughout modern functional analysis.

List of 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.

About the author

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.

Summary

This book covers the spectral theory of Toeplitz forms and Wiener–Hopf integral operators and their applications in harmonic and functional analysis. With exercises and solutions, historical background, and surveys of the latest results, this is an essential source on Toeplitz theory for students and researchers alike.

Product details

• Authors: Nikolai Nikolski, Nikolaï Nikolski, Nikolai (Universite De Bordeaux) Nikolski
• Assisted by: Daniele Gibbons (Translation), Danièle Gibbons (Translation), Greg Gibbons (Translation)
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.01.2020
• EAN: 9781107198500
• ISBN: 978-1-107-19850-0
• No. of pages: 450
• Series: Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced Mathematics; Cambridge Studies in Advanced
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Mathematical Analysis, Numerical analysis, Complex analysis, complex variables, Real analysis, real variables