Operator Theory in Function Spaces - Kehe Zhu

Operator Theory in Function Spaces

(Autor)

Buch | Hardcover
348 Seiten
2007 | 2nd Revised edition
American Mathematical Society (Verlag)
978-0-8218-3965-2 (ISBN)
109,95 inkl. MwSt
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Covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. This book studies analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study.
This book covers Toeplitz operators, Hankel operators, and composition operators on both the Bergman space and the Hardy space. The setting is the unit disk and the main emphasis is on size estimates of these operators: boundedness, compactness, and membership in the Schatten classes. Most results concern the relationship between operator-theoretic properties of these operators and function-theoretic properties of the inducing symbols. Thus a good portion of the book is devoted to the study of analytic function spaces such as the Bloch space, Besov spaces, and BMOA, whose elements are to be used as symbols to induce the operators we study. The book is intended for both research mathematicians and graduate students in complex analysis and operator theory. The prerequisites are minimal; a graduate course in each of real analysis, complex analysis, and functional analysis should sufficiently prepare the reader for the book. Exercises and bibliographical notes are provided at the end of each chapter. These notes will point the reader to additional results and problems. Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His previous books include Theory of Bergman Spaces (Springer, 2000, with H. Hedenmalm and B. Korenblum) and Spaces of Holomorphic Functions in the Unit Ball (Springer, 2005). His current research interests are holomorphic function spaces and operators acting on them.

Bounded linear operators Interpolation of Banach spaces Integral operators on $L^p$ spaces Bergman spaces Bloch and Besov spaces The Berezin transform Toeplitz operators on the Bergman space Hankel operators on the Bergman space Hardy spaces and BMO Hankel operators on the Hardy space Composition operators Bibliography Index.

Erscheint lt. Verlag 30.5.2007
Reihe/Serie Mathematical Surveys and Monographs
Verlagsort Providence
Sprache englisch
Gewicht 798 g
Themenwelt Mathematik / Informatik Mathematik Analysis
ISBN-10 0-8218-3965-9 / 0821839659
ISBN-13 978-0-8218-3965-2 / 9780821839652
Zustand Neuware
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