Graduate Texts in Mathematics

Several Complex Variables and Banach Algebras

Authors: Alexander, Herbert, Wermer, John

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About this Textbook

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.

Table of contents (27 chapters)

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-0-387-22586-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $99.00
price for USA
  • ISBN 978-0-387-98253-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $99.00
price for USA
  • ISBN 978-1-4757-7163-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Several Complex Variables and Banach Algebras
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
35
Copyright
1998
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-0-387-22586-9
DOI
10.1007/b97591
Hardcover ISBN
978-0-387-98253-3
Softcover ISBN
978-1-4757-7163-3
Series ISSN
0072-5285
Edition Number
3
Number of Pages
XII, 256
Topics