The Theory of H(b) Spaces: Volume 2 (New Mathematical Monographs)
Cambridge University Press, 10/20/2016
EAN 9781107027787, ISBN10: 1107027780
Hardcover, 640 pages, 23.6 x 15.8 x 4.5 cm
Language: English
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(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) ⊂ H(b̅) ⊂ 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.