Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Other
- Figures
- 1 Why Toeplitz–Hankel? Motivations and Panorama
- 2 Hankel and Toeplitz: Sibling 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
- Backmatter
- Index
1 - Why Toeplitz–Hankel? Motivations and Panorama
Published online by Cambridge University Press: 06 December 2019
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Other
- Figures
- 1 Why Toeplitz–Hankel? Motivations and Panorama
- 2 Hankel and Toeplitz: Sibling 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
- Backmatter
- Index
Summary
Four cornerstones of the theory of Toeplitz operators: the Riemann–Hilbert problem (RHP), the singular integral operators (SIO), the Wiener–Hopf operators (WHO), and last (but not least) the Toeplitz matrices and operators (TMO) (strictly speaking, compressions of multiplication operators).
The founding contributions of Bernhard Riemann, David Hilbert, George Birkhoff, Otto Toeplitz, Gábor Szegő, Norbert Wiener, and Eberhard Hopf.
The modern and post-modern periods of the theory.
- Type
- Chapter
- Information
- Toeplitz Matrices and Operators , pp. 1 - 30Publisher: Cambridge University PressPrint publication year: 2020