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The Theory of <I>H</I>(<I>b</I>) Spaces
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    Rosenfeld, Joel A. 2016. The Sarason sub-symbol and the recovery of the symbol of densely defined Toeplitz operators over the Hardy space. Journal of Mathematical Analysis and Applications, Vol. 440, Issue. 2, p. 911.

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Book description

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.

Reviews

'The monograph contains numerous references to original papers, as well as numerous exercises. This monograph may be strongly recommended as a good introduction to this interesting and intensively developing branch of analysis …'

Vladimir S. Pilidi Source: Zentralblatt MATH

'As with Volume 1, chapter notes outline historical development, and an extensive bibliography cites substantial work done in the area since 2000.'

Joseph D. Lakey Source: MathSciNet

‘… 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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