Several Complex Variables and Banach Algebras

• Main Authors: Alexander, Herbert (Author), Wermer, John (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 1998.
• Edition: Third Edition.
• Series: Graduate Texts in Mathematics, 35
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Analysis.

Many connections have been found between the theory of analytic functions of one or more complex variables and the study of commutative Banach algebras. While function theory has often been employed to answer algebraic questions such as the existence of idempotents in a Banach algebra, concepts aris...

Table of Contents:

• Preliminaries and Notation
• Classical Approximation Theorems
• Operational Calculus in One Variable
• Differential Forms
• The -Operator
• The Equation
• The Oka-Weil Theorem
• Operational Calculus in Several Variables
• The Šilov Boundary
• Maximality and Radó’s Theorem
• Maximum Modulus Algebras
• Hulls of Curves and Arcs
• Integral Kernels
• Perturbations of the Stone?Weierstrass Theorem
• The First Cohomology Group of a Maximal Ideal Space
• The -Operator in Smoothly Bounded Domains
• Manifolds Without Complex Tangents
• Submanifolds of High Dimension
• Boundaries of Analytic Varieties
• Polynomial Hulls of Sets Over the Circle
• Areas
• Topology of Hulls
• Pseudoconvex sets in ?n
• Examples
• Historical Comments and Recent Developments
• Solutions to Some Exercises.