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Mathematics - Analysis | Analysis on Fock Spaces

Analysis on Fock Spaces

Series: Graduate Texts in Mathematics, Vol. 263

Zhu, Kehe

2012, X, 346 p.

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  • Fills the gap in existing literature concerning the natural Lp spaces of analytic functions
  • First book on the market concerning Fock spaces, summarizing the most important results and techniques in one place, so that new comers, especially graduate students, have a convenient reference to the subject
  • Features new and simpler proofs than the existing ones in the literature
  • Includes exercises of various levels at the end of every chapter
  • Contains an extensive bibliography

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.

Content Level » Graduate

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

Related subjects » Analysis

Table of contents 

Preface.- Chapter 1. Preliminaries.- Chapter 2. Fock Spaces.- Chapter 3. The Berezin Transform and BMO.- Chapter 4. Interpolating and Sampling Sequences.- Chapter 5. Zero Sets for Fock Spaces.- Chapter 6. Toeplitz Operators.- Chapter 7. Small Hankel Operators.- Chapter 8. Hankel Operators.- References.- Index.

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