Analysis on Fock Spaces (Graduate Texts in Mathematics, Vol. 263) (Graduate Texts in Mathematics (263))

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. Front Matter....Pages i-x Preliminaries....Pages 1-29 Fock Spaces....Pages 31-92 The Berezin Transform and BMO....Pages 93-135 Interpolating and Sampling Sequences....Pages 137-191 Zero Sets for Fock Spaces....Pages 193-212 Toeplitz Operators....Pages 213-266 Small Hankel Operators....Pages 267-285 Hankel Operators....Pages 287-329 Back Matter....Pages 331-344 Preliminaries -- Fock Spaces -- The Berezin Transform And Bmo -- Interpolating And Sampling Sequences -- Zero Sets For Fock Spaces -- Toeplitz Operators -- Small Hankel Operators -- Hankel Operators. Kehe Zhu. Includes Bibliographical References (p. 331-340) And Index.