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The Theory of H(b) Spaces
Emmanuel Fricain ; Javad Mashreghi
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Últimas novedades matemáticas
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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. |
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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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