Analysis on Fock Spaces [electronic resource] / by Kehe Zhu.

By: Zhu, Kehe [author.]
Contributor(s): SpringerLink (Online service)
Material type: TextTextSeries: Graduate Texts in Mathematics: 263Publisher: Boston, MA : Springer US : Imprint: Springer, 2012Description: X, 346 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9781441988010Subject(s): Mathematics | Functional analysis | Functions of complex variables | Operator theory | Mathematics | Functions of a Complex Variable | Operator Theory | Several Complex Variables and Analytic Spaces | Functional AnalysisAdditional physical formats: Printed edition:: No titleDDC classification: 515.9 LOC classification: QA331-355Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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