The Theory of H(b) Spaces Volume 2 [Hardcover]

In two volumes, this comprehensive treatment covers all that is needed to understand and appreciate this beautiful branch of mathematics.This comprehensive treatment in two volumes is accessible to graduate students as well as researchers. It covers all of the preliminary subjects required to fully understand and appreciate this beautiful branch of mathematics, such as Hardy spaces, Fourier analysis and Carleson measures. Volume 2 focuses on the central theory.This comprehensive treatment in two volumes is accessible to graduate students as well as researchers. It covers all of the preliminary subjects required to fully understand and appreciate this beautiful branch of mathematics, such as Hardy spaces, Fourier analysis and Carleson measures. Volume 2 focuses on the central theory.An H(b) space is defined as a collection of analytic functions that 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. Volume 1 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. Volume 2 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.Preface; 16. The spaces M(A) and H(A); 17. Hilbert spaces inside H2; 18. The structure of H(b) and H(b ); 19. Geometric representation of H(b) spaces; 20. Representation theorems for H(b) and H(b); 21. Angular derivatives of H(b) functions; 22. Bernstein-type inequalities; 23. H(b) spaces generatel³‡