The theory of H(b) spaces. Volume 2 / Emmanuel Fricain, Université Lille I, Javad Mashreghi, Université Laval, Quebec.

Format:

Book

Author/Creator:

Fricain, Emmanuel, 1971- author.

Mashreghi, Javad, author.

Series:

Cambridge books online.

New mathematical monographs ; 21.

New mathematical monographs ; 21

Language:

English

Subjects (All):

Hilbert space.

Hardy spaces.

Analytic functions.

Linear operators.

Physical Description:

1 online resource (xix, 619 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2016.

System Details:

text file

PDF

Summary:

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.

Contents:

Machine generated contents note: 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 KT; 15. Bases of reproducing kernels and interpolation; Bibliography; Index.

Notes:

Title from publisher's bibliographic system (viewed on 27 Oct 2016).

Other Format:

Print version:

ISBN:

9781139226769

Access Restriction:

Restricted for use by site license.