The Theory of H(b) Spaces
The Theory of <I>H</I>(<I>b</I>) Spaces
$215.00
USDAn H(b) space is defined as a collection of analytic functions which are in the image of an operator. The theory of H(b) spaces bridges two classical subjects: complex analysis and operator theory, which makes it both appealing and demanding. The first volume of this comprehensive treatment is devoted to the preliminary subjects required to understand the foundation of H(b) spaces, such as Hardy spaces, Fourier analysis, integral representation theorems, Carleson measures, Toeplitz and Hankel operators, various types of shift operators, and Clark measures. The second volume focuses on the central theory. Both books are accessible to graduate students as well as researchers: each volume contains numerous exercises and hints, and figures are included throughout to illustrate the theory. Together, these two volumes provide everything the reader needs to understand and appreciate this beautiful branch of mathematics.
- Covers all of the material required to understand the theory and its foundations
- Suitable as a textbook for graduate courses
- Contains over 200 exercises to test students' grasp of the material covered
Reviews & endorsements
'This two volume monograph is a compendium of the H(b) spaces that will be of interest to both graduate students and practicing mathematicians interested in function-theoretic operator theory. There are 31 chapters between the two volumes and a detailed bibliography consisting of 766 entries. The first volume is devoted to general function-theoretic operator theory (and indeed is a useful reference in its own right) while the second volume is more specialized and contains an in-depth survey of H(b)H(b) theory and related ideas.' Steve Deckelman, MAA Reviews
'… designed for a person who wants to learn the theory of these spaces and understand the state of the art in the area. All major results are included. In some situations the original proofs are provided, while in other cases they provide the 'better' proofs that have become available since. The books are designed to be accessible to both experts and newcomers to the area. Comments at the end of each section are very helpful, and the numerous exercises were clearly chosen to help master some of the techniques and tools used … In sum, these are excellent books that are bound to become standard references for the theory of H(b) spaces.' Bulletin of the American Mathematical Society
Product details
May 2016Hardback
9781107027770
702 pages
236 × 158 × 50 mm
1.2kg
30 b/w illus. 320 exercises
Available
Table of Contents
- List of figures
- Preface
- List of symbols
- Important conventions
- 1. *Normed linear spaces and their operators
- 2. Some families of operators
- 3. Harmonic functions on the open unit disc
- 4. Analytic functions on the open unit disc
- 5. The corona problem
- 6. Extreme and exposed points
- 7. More advanced results in operator theory
- 8. The shift operator
- 9. Analytic reproducing kernel Hilbert spaces
- 10. Bases in Banach spaces
- 11. Hankel operators
- 12. Toeplitz operators
- 13. Cauchy transform and Clark measures
- 14. Model subspaces KΘ
- 15. Bases of reproducing kernels and interpolation
- Bibliography
- Index.
