Banach Algebras and Several Complex Variables / John Wermer

Wermer, John

ISBN 10: 0387901604 / ISBN 13: 9780387901602

Published by New York, NY : Springer, 1976

About this Item

Fine copy in the original colour-printed boards. Remains particularly well-preserved overall; tight, bright, clean and strong. Physical description; 161 pp. Notes; Graduate texts in mathematics series, 35. Includes bibliographical b222breferences (157-160) and index. Contents; 1. Preliminaries and Notations -- 2. Classical Approximation Theorems -- 3. Operational Calculus in One Variable -- 4. Differential Forms -- 5. The ??-Operator -- 6. The Equation ??u = -- 7. The Oka Weil Theorem -- 8. Operational Calculus in Several Variables -- 9. The ilov Boundary -- 10. Maximality and Radó s Theorem -- 11. Analytic Structure -- 12. Algebras of Analytic Functions -- 13. Approximation on Curves in Cn -- 14. Uniform Approximation on Disks in Cn -- 15. The First Cohomology Group of a Maximal Ideal Space -- 16. The ??-Operator in Smoothly Bounded Domains -- 17. Manifolds without Complex Tangents -- 18. Submanifolds of High Dimension -- 19. Generators -- 20. The Fibers over a Plane Domain -- 21. Examples of Hulls -- 22. Solutions to Some Exercises. Subjects; Banach algebras. Functions of several complex variables. Mathematics. 1 Kg.

Seller Inventory # 385168

Bibliographic Details

• Title: Banach Algebras and Several Complex Variables / John Wermer
• Publisher: New York, NY : Springer
• Publication Date: 1976
• Language: English
• ISBN 10: 0387901604
• ISBN 13: 9780387901602
• Binding: Hardcover
• Edition: 2nd edition.
• Weight: 1 kilogram

About this title

Synopsis

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 arising from the study of Banach algebras including the maximal ideal space, the Silov boundary, Geason parts, etc. have led to new questions and to new methods of proofs in function theory. This book is concerned with developing 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. The third edition of this book 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 containing commentaries on history and recent developments and an updated and expanded reading list.