Opis: The Theory of H(b) Spaces: Volume 1 - Javad Mashreghi, Emmanuel Fricain

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.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 KTHETA; 15. Bases of reproducing kernels and interpolation; Bibliography; Index.

Szczegóły: The Theory of H(b) Spaces: Volume 1 - Javad Mashreghi, Emmanuel Fricain

Tytuł: The Theory of H(b) Spaces: Volume 1
Autor: Javad Mashreghi, Emmanuel Fricain
Wydawnictwo: Cambridge University Press
ISBN: 9781107027770
Rok wydania: 2000
Ilość stron: 702
Oprawa: Twarda
Waga: 1.19 kg

Recenzje: The Theory of H(b) Spaces: Volume 1 - Javad Mashreghi, Emmanuel Fricain