TY  - BOOK
AU  - Fricain, Emmanuel,
AU  - Fricain, Emmanuel
AU  - Mashreghi, Javad
TI  - The Theory of H(b) spaces 
T2  - New mathematical monographs, 20
SN  - 9781107027770
U1  - 515.733 FRI 
PY  - 2016///
CY  - Cambridge
PB  -  Cambridge University Press, 
KW  - Mathematics
KW  -  Analysis
KW  - Hilbert space
KW  - Hardy spaces
KW  - Linear operators
KW  - Analytic functions
KW  - MATHEMATICS -- Mathematical Analysis
N1  - Normed linear spaces and their operators --
Some families of operators --
Harmonic functions on the open unit disk --
Hardy spaces --
More function spaces --
Extreme and exposed points --
More advanced results in operator theory --
The shift operator --
Analytic reproducing kernel Hilbert spaces --
Bases in Banach spaces --
Hankel operators --
Toeplitz operators --
Cauchy transform and Clark measures --
Model subspaces Ko --
Bases of reproducing kernels and interpolation
N2  - 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
ER  -