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9781107027770

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'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, 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.' Bulletin of the American Mathematical Society '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, 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.' Bulletin of the American Mathematical Society

'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, MAA Reviews

Author Information

Emmanuel Fricain is a Professor in the Laboratoire Paul Painlevé at Université Lille 1. A part of his research focuses on the interaction between complex analysis and operator theory, which is the main matter of this book. He has a long experience of teaching numerous graduate courses on different aspects of analytic Hilbert spaces and has published several papers on H(b) spaces in high-quality journals, making him a world specialist in this subject. Javad Mashreghi is a Professor of Mathematics at Laval University, Québec, where he has been selected Star Professor of the Year five times for excellence in teaching. His main fields of interest are complex analysis, operator theory and harmonic analysis.

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