Toeplitz Matrices and Operators

ISBN-13: 9781107198500 / Angielski / Twarda / 2020 / 450 str.

Nikolai Nikolski; Daniele Gibbons; Greg Gibbons

Opis

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.

Recenzje

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

Spis treści

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.