Toeplitz Matrices and Operators

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

Nikolaï Nikolski (Author), Danièle Gibbons (Translated by), Greg Gibbons (Translated by)

9781107198500, Cambridge University Press

Hardback, published 2 January 2020

450 pages, 43 b/w illus. 40 exercises
23.5 x 15.6 x 2.9 cm, 0.75 kg

'I strongly recommend it for both students and experts. The unique style of the book will captivate the reader.' Maria T. Nowak, MathSciNet

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, 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.

Subject Areas: Numerical analysis [PBKS], Complex analysis, complex variables [PBKD], Real analysis, real variables [PBKB]