Banach Spaces Of Analytic Functions
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Banach Spaces of Analytic Functions
Author: Kenneth Hoffman
language: en
Publisher: Courier Corporation
Release Date: 2007-02-27
A classic of pure mathematics, this advanced graduate-level text explores the intersection of functional analysis and analytic function theory. Close in spirit to abstract harmonic analysis, it is confined to Banach spaces of analytic functions in the unit disc. The author devotes the first four chapters to proofs of classical theorems on boundary values and boundary integral representations of analytic functions in the unit disc, including generalizations to Dirichlet algebras. The fifth chapter contains the factorization theory of Hp functions, a discussion of some partial extensions of the factorization, and a brief description of the classical approach to the theorems of the first five chapters. The remainder of the book addresses the structure of various Banach spaces and Banach algebras of analytic functions in the unit disc. Enhanced with 100 challenging exercises, a bibliography, and an index, this text belongs in the libraries of students, professional mathematicians, as well as anyone interested in a rigorous, high-level treatment of this topic.
Banach Spaces of Analytic Functions
Author: Thomas H. MacGregor
language: en
Publisher: American Mathematical Soc.
Release Date: 2008
This volume is focused on Banach spaces of functions analytic in the open unit disc, such as the classical Hardy and Bergman spaces, and weighted versions of these spaces. Other spaces under consideration here include the Bloch space, the families of Cauchy transforms and fractional Cauchy transforms, BMO, VMO, and the Fock space. Some of the work deals with questions about functions in several complex variables.
Banach Spaces of Analytic Functions and Absolutely Summing Operators
Author: Aleksander Pełczyński
language: en
Publisher: American Mathematical Soc.
Release Date: 1977-12-31
This book surveys results concerning bases and various approximation properties in the classical spaces of analytical functions. It contains extensive bibliographical comments.