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  1. Home
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  3. The Theory of H(b) Spaces
  • Cited by 14
Publisher:
Cambridge University Press
Online publication date:
May 2016
Print publication year:
2016
Online ISBN:
9781139226752
DOI:
https://doi.org/10.1017/CBO9781139226752
Subjects:
Mathematics (general), Mathematics, Abstract Analysis
Series:
New Mathematical Monographs (20)
Information

Book 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.

Reviews

'This two volume monograph is a compendium of the H(b) spaces that will be of interest to both graduate students and practicing mathematicians interested in function-theoretic operator theory. There are 31 chapters between the two volumes and a detailed bibliography consisting of 766 entries. The first volume is devoted to general function-theoretic operator theory (and indeed is a useful reference in its own right) while the second volume is more specialized and contains an in-depth survey of H(b)H(b) theory and related ideas.'

Steve Deckelman Source: MAA Reviews

‘… designed for a person who wants to learn the theory of these spaces and understand the state of the art in the area. All major results are included. In some situations the original proofs are provided, while in other cases they provide the 'better' proofs that have become available since. The books are designed to be accessible to both experts and newcomers to the area. Comments at the end of each section are very helpful, and the numerous exercises were clearly chosen to help master some of the techniques and tools used … In sum, these are excellent books that are bound to become standard references for the theory of H(b) spaces.’

Source: Bulletin of the American Mathematical Society

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