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Analysis on Fock Spaces

  • Kehe Zhu

Part of the Graduate Texts in Mathematics book series (GTM, volume 263)

Table of contents

  1. Front Matter
    Pages i-x
  2. Kehe Zhu
    Pages 1-29
  3. Kehe Zhu
    Pages 31-92
  4. Kehe Zhu
    Pages 93-135
  5. Kehe Zhu
    Pages 137-191
  6. Kehe Zhu
    Pages 193-212
  7. Kehe Zhu
    Pages 213-266
  8. Kehe Zhu
    Pages 267-285
  9. Kehe Zhu
    Pages 287-329
  10. Back Matter
    Pages 331-344

About this book

Introduction

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 newcomers, 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.

Keywords

Berezin transform Fock spaces Hankel operators Schatten classes Toeplitz operators entire functions interpolating sequences sampling sequences zero sets

Authors and affiliations

  • Kehe Zhu
    • 1
  1. 1.Department of Mathematics and StatisticsState University of New York, AlbanyAlbanyUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-8801-0
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, Boston, MA
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-8800-3
  • Online ISBN 978-1-4419-8801-0
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site