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The Theory of H(b) Spaces
Emmanuel Fricain ; Javad Mashreghi
The Theory of H(b) Spaces
ean9781107027770
temáticaMATEMÁTICAS
año Publicación2013
idiomaINGLÉS
editorialCAMBRIDGE UP. ESPAÑA
formatoCARTONÉ


114,95 €


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matemáticas
An 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.
indíce
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 KT
15. Bases of reproducing kernels and interpolation
Bibliography
Index.
AuthorsEmmanuel Fricain, Université Lyon I
Emmanuel Fricain is Maître de conférences at the Institut Camille Jordan, Université Lyon I. A part of his research focuses on the interaction between complex analysis and operator theory, which is the main matter of this book. He has a long experience of teaching numerous graduate courses on different aspects of analytic Hilbert spaces and has published several papers on H(b) spaces in high-quality journals, making him a world specialist in this subject.
Javad Mashreghi, Université Laval, Québec
Javad Mashreghi is a Professor of Mathematics at Laval University, Québec, where he has been selected Star Professor of the Year five times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis.

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