Analysis on Fock spaces / Kehe Zhu
Type de document : Livre numériqueCollection : Graduate texts in mathematics, 263Langue : anglais.Éditeur : Berlin : Springer, cop. 2012ISBN: 9781441988003.ISSN: 0072-5285.Sujet MSC : 30H20, Functions of a complex variable - Spaces and algebras of analytic functions, Bergman spaces and Fock spaces30D15, Entire and meromorphic functions of one complex variable, and related topics, Special classes of entire functions of one complex variable and growth estimates
46E20, Functional analysis - Linear function spaces and their duals, Hilbert spaces of continuous, differentiable or analytic functions
47B10, Operator theory - Special classes of linear operators, Linear operators belonging to operator ideals
47B35, Operator theory - Special classes of linear operators, Toeplitz operators, Hankel operators, Wiener-Hopf operatorsEn-ligne : Springerlink | zbMath | MSN
As explained in the preface, this book is intended to provide a convenient reference to Fock spaces.
The book begins with preliminary results about entire functions, lattices in the complex plane, pseudodifferential operators, and the Heisenberg group. The reader who is familiar with these materials may skip this chapter.
The second chapter introduces the basics of the Fock space: reproducing kernel, integral representation, duality, complex interpolation, atomic decomposition, translation invariance and a version of the maximum principle.
The third chapter is devoted to the study of the Berezin transformation and bounded mean oscillation (BMO) on the complex plane. Since the Berezin transform is closely related to the notion of Carleson measures, the discussion of Fock-Carleson measures is also included in this chapter.
The fourth chapter is devoted to the study of characterizations of interpolating and sampling sequences for the Fock space.
In the fifth chapter, the author studies zero sets for the Fock space.
The remaining chapters (Chapter 6–8) are devoted to the study of three kinds of operators: Toeplitz, small Hankel, and Hankel operators.
Each chapter ends with a series of exercises. The material is presented in a pedagogical way. The reference list contains 259 relevant items. This book is well written and it is a good reference for graduate students who are interested in Fock spaces. (zbMath)
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