Analysis on Fock Spaces

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Springer Science & Business Media, May 26, 2012 - Mathematics - 346 pages
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Several natural Lp spaces of analytic functions have been widely studied in the past few decades, including Hardy spaces, Bergman spaces, and Fock spaces. The terms “Hardy spaces” and “Bergman spaces” are by now standard and well established. But the term “Fock spaces” is a different story.

Numerous excellent books now exist on the subject of Hardy spaces. Several books about Bergman spaces, including some of the author’s, have also appeared in the past few decades. But there has been no book on the market concerning the Fock spaces. The purpose of this book is to fill that void, especially when many results in the subject are complete by now. This book presents important results and techniques summarized in one place, so that new comers, especially graduate students, have a convenient reference to the subject.

This book contains proofs that are new and simpler than the existing ones in the literature. In particular, the book avoids the use of the Heisenberg group, the Fourier transform, and the heat equation. This helps to keep the prerequisites to a minimum. A standard graduate course in each of real analysis, complex analysis, and functional analysis should be sufficient preparation for the reader.

 

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Contents

Chapter 1 Preliminaries
1
Chapter 2 Fock Spaces
31
Chapter 3 The Berezin Transform and BMO
93
Chapter 4 Interpolating and Sampling Sequences
136
Chapter 5 Zero Sets for Fock Spaces
193
Chapter 6 Toeplitz Operators
213
Chapter 7 Small Hankel Operators
267
Chapter 8 Hankel Operators
286
References
331
Index
341
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About the author (2012)

Kehe Zhu is a professor of mathematics at the State University of New York at Albany. His research areas include operators on holomorphic function spaces, complex analysis, and operator theory and operator algebras.

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