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Several Complex Variables & Banach Algebras, 3rd Edition

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Several Complex Variables & Banach Algebras, 3rd Edition Cover

 

Synopses & Reviews

Publisher Comments:

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.

Description:

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.

Product Details

ISBN:
9780387982533
Author:
Herbert Alexander and John Wermer
Publisher:
Springer
Author:
Wermer, J.
Author:
Wermer, John
Author:
Alexander, H.
Author:
Alexander, Herbert
Location:
New York, NY
Subject:
Algebra - Linear
Subject:
Vector Analysis
Subject:
Banach algebras
Subject:
Functions of several complex variables
Subject:
Mathematical Analysis
Subject:
Analysis
Subject:
Mathematics : Vector Analysis
Subject:
Mathematics
Subject:
Language, literature and biography
Subject:
mathematics and statistics
Subject:
Global analysis (Mathematics)
Copyright:
Edition Number:
3rd ed.
Edition Description:
3rd ed. 1998
Series:
Graduate texts in mathematics ;
Series Volume:
535
Publication Date:
19971120
Binding:
HARDCOVER
Language:
English
Illustrations:
Y
Pages:
268
Dimensions:
235 x 155 mm 500 gr

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