- STAFF PICKS
- GIFTS + GIFT CARDS
- SELL BOOKS
- FIND A STORE
Ships in 1 to 3 days
available for shipping or prepaid pickup only
Available for In-store Pickup
in 7 to 12 days
This title in other editions
Other titles in the Graduate Texts in Mathematics series:
Several Complex Variables & Banach Algebras, 3rd Editionby Herbert Alexander and John Wermer
Synopses & Reviews
A development of some of the principal applications of function theory in several complex variables to Banach algebras. The authors do not presuppose any knowledge of several complex variables on the part of the reader, and all relevant material is developed within the text. Furthermore, the book deals with problems of uniform approximation on compact subsets of the space of n complex variables. This third edition contains new material on maximum modulus algebras and subharmonicity, the hull of a smooth curve, integral kernels, perturbations of the Stone-Weierstrass Theorem, boundaries of analytic varieties, polynomial hulls of sets over the circle, areas, and the topology of hulls. The authors have also included a new chapter commenting on history and recent developments, as well as an updated and expanded reading list.
Includes bibliographical references (p. 241-249) and index.
Table of Contents
Preliminaries and Notations.- Classical Approximation Theorems.- Operational Calculus in One Variable.- Differential Forms.- The *-Operator.- The Equation.- The Oka-Weil Theorem.- Operational Calculus in Several Variables.- The Silov Boundary.- Maximality and Rado'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 with Complex Tangents.- Submanifolds of High Dimension.- Boundaries of Analytic Varieties.- Polynomial Hulls of Sets over the Circle.- Areas.- Topology of Hulls.- Pseudoconvex Sets in Cn.- Examples.- Historical Comments and Recent Developments.- Appendix.- Solutions of Some Exercises. Bibliography. Additional Bibliography. Index.
What Our Readers Are Saying
Other books you might like
History and Social Science » Politics » General