rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Several complex variables and Banach algebras
  name:
    name part: Alexander, Herbert.
    role:
      role term: creator
  name:
    name part: Wermer, John.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 1998
    edition: 3rd ed.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xii, 253 pages)
  abstract: 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: 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.
  note: Herbert Alexander, John Wermer.
  note: Revised edition of: Banach algebras and several complex variables / John Wermer. 2nd edition 1976.
  note: Electronic resource.
  note: Includes bibliographical references (pages 241-249) and index.
  subject:
    topic: Banach algebras
  subject:
    topic: Functions of several complex variables
  subject:
    topic: Mathematics
  subject:
    topic: Banach, Algèbres de
  subject:
    topic: Fonctions de plusieurs variables complexes
  subject:
    topic: MATHEMATICS
    topic: Algebra
    topic: Linear
  subject:
    topic: Banach algebras
  subject:
    topic: Functions of several complex variables
  classification: QA326 .W47 1998eb
  classification: 512/.55
  related item:
    title info:
      title: Banach algebras and several complex variables
    name:
      name part: Wermer, John.
  related item:
    title info:
      title: Several complex variables and Banach algebras
    name:
      name part: Alexander, Herbert.
    origin info:
      publisher: New York : Springer, ©1998
      edition: 3rd ed.
    identifier: (DLC) 97016661
  related item:
    title info:
      title: Graduate texts in mathematics ; 35
  identifier: 0387225862
  identifier: 9780387225869
  identifier: 058547804X
  identifier: 9780585478043
  identifier: 9780387982533
  identifier: 0387982531
  identifier: http://proxy.library.tamu.edu/login
  record info:
    record content source: VVN
    record creation date: 020717
    record change date: 20260422173311.8
    record identifier: in00003514230
    language of cataloging:
      language term: eng