The theory of H(b) spaces. Vol.2

Description

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 Content: Preface 16. The spaces M(A) and H(A) 17. Hilbert spaces inside H2 18. The structure of H(b) and H(bÌ ) 19. Geometric representation of H(b) spaces 20. Representation theorems for H(b) and H(bÌ ) 21. Angular derivatives of H(b) functions 22. Bernstein-type inequalities 23. H(b) spaces generated by a nonextreme symbol b 24. Operators on H(b) spaces with b nonextreme 25. H(b) spaces generated by an extreme symbol b 26. Operators on H(b) spaces with b extreme 27. Inclusion between two H(b) spaces 28. Topics regarding inclusions M(a) â H(bÌ ) â H(b) 29. Rigid functions and strongly exposed points of H1 30. Nearly invariant subspaces and kernels of Toeplitz operators 31. Geometric properties of sequences of reproducing kernels References Symbols index Index.