Banach Spaces of Analytic Functions

Banach Spaces of Analytic Functions

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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.Kenneth Hoffman. for each 1a#39; in H1. Conversely, if the sum is finite for each f, the rule Tf = {|f(zk)|(1 aquot; lzklzlla#39; defines a linear mapping of H1 into the Banach space 61 of all ... The condition M alt; 00 says simply that T is a bounded linear transformation from H1 to Ap1. ... task to a weighted interpolation problem for H2 functions.

Title:Banach Spaces of Analytic Functions
Author:Kenneth Hoffman
Publisher:Courier Corporation - 2014-06-10


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