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: Harmonic function theory
  name:
    name part: Axler, Sheldon Jay.
    role:
      role term: creator
  name:
    name part: Bourdon, Paul.
  name:
    name part: Ramey, Wade.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  genre: bibliography
  genre: Electronic books.
  origin info:
    place:
      place term: nyu
    date issued: 2001
    edition: 2nd ed.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: remote
    extent: 1 online resource (xi, 259 pages) : illustrations.
  abstract: Harmonic functions - the solutions of Laplace's equation - play a crucial role in many areas of mathematics, physics, and engineering. Avoiding the disorganization and inconsistent notation of other expositions, the authors approach the field from a more function-theoretic perspective, emphasizing techniques and results that will seem natural to mathematicians comfortable with complex function theory and harmonic analysis; prerequisites for the book are a solid foundation in real and complex analysis together with some basic results from functional analysis. Topics covered include: basic properties of harmonic functions defined on subsets of Rn, including Poisson integrals; properties bounded functions and positive functions, including Liouville's and Cauchy's theorems; the Kelvin transform; Spherical harmonics; hp theory on the unit ball and on half-spaces; harmonic Bergman spaces; the decomposition theorem; Laurent expansions and classification of isolated singularities; and boundary behavior. An appendix describes routines for use with MATHEMATICA to manipulate some of the expressions that arise in the study of harmonic functions.
  table of contents: Basic Properties of Harmonic Functions -- Bounded Harmonic Functions -- Positive Harmonic Functions -- The Kelvin Transform -- Harmonic Polynomials -- Harmonic Hardy Spaces -- Harmonic Functions on Half-Spaces -- Harmonic Bergman Spaces -- The Decomposition Theorem -- Annular Regions -- The Dirichlet Problem and Boundary Behavior -- Volume, Surface Area, and Integration on Spheres -- Harmonic Function Theory and Mathematica -- References -- Symbol Index -- Index.
  note: Sheldon Axler, Paul Bourdon, Wade Ramey.
  note: Electronic resource.
  note: Includes bibliographical references (pages 249-250) and indexes.
  subject:
    topic: Harmonic functions
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Fonctions harmoniques
  subject:
    topic: MATHEMATICS
    topic: Calculus
  subject:
    topic: MATHEMATICS
    topic: Mathematical Analysis
  subject:
    topic: Harmonic functions
  subject:
    topic: Harmonic functions
  subject:
    topic: Fonctions harmoniques
  subject:
    topic: Electronic books
  classification: QA405 .A95 2001eb
  classification: 515/.53
  classification: O174. 3
  related item:
    title info:
      title: Harmonic function theory
    name:
      name part: Axler, Sheldon Jay.
    origin info:
      publisher: New York : Springer, 2001
      edition: 2nd ed.
    identifier: (DLC) 00053771
    identifier: (OCoLC)45315455
  related item:
    title info:
      title: Graduate texts in mathematics ; 137
  identifier: 0387215271 (electronic bk.)
  identifier: 9780387215273 (electronic bk.)
  identifier: 9781475781373 (electronic bk.)
  identifier: 1475781377 (electronic bk.)
  identifier: 0387952187
  identifier: 9780387952185
  identifier: https://proxy.library.tamu.edu/login
  related item:
    location:
      url: https://proxy.library.tamu.edu/login
  record info:
    record content source: N$T
    record creation date: 040809
    record change date: 20220105142442.0
    record identifier: in00002035336
    language of cataloging:
      language term: eng