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: Geometric Analysis of the Bergman Kernel and Metric
  name:
    name part: Krantz, Steven G.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2013
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XIII, 292 p. 7 illus. online resource.
  abstract: This text provides a masterful and systematic treatment of all the basic analytic and geometric aspects of Bergman's classic theory of the kernel and its invariance properties. These include calculation, invariance properties, boundary asymptotics, and asymptotic expansion of the Bergman kernel and metric. Moreover, it presents a unique compendium of results with applications to function theory, geometry, partial differential equations, and interpretations in the language of functional analysis, with emphasis on the several complex variables context. Several of these topics appear here for the first time in book form. Each chapter includes illustrative examples and a collection of exercises which will be of interest to both graduate students and experienced mathematicians. Graduate students who have taken courses in complex variables and have a basic background in real and functional analysis will find this textbook appealing. Applicable courses for either main or supplementary usage include those in complex variables, several complex variables, complex differential geometry, and partial differential equations. Researchers in complex analysis, harmonic analysis, PDEs, and complex differential geometry will also benefit from the thorough treatment of the many exciting aspects of Bergman's theory.
  table of contents: Preface -- 1. Introductory Ideas -- 2. The Bergman Metric -- 3. Geometric and Analytic Ideas -- 4. Partial Differential Equations -- 5. Further Geometric Explorations -- 6. Additional Analytic Topics -- 7. Curvature of the Bergman Metric -- 8. Concluding Remarks -- Table of Notation -- Bibliography -- Index.
  note: by Steven G. Krantz.
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical analysis
  subject:
    topic: Analysis (Mathematics)
  subject:
    topic: Functional analysis
  subject:
    topic: Partial differential equations
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematics
  subject:
    topic: Analysis
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Functional Analysis
  subject:
    topic: Differential Geometry
  classification: QA299.6-433
  classification: 515
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Graduate Texts in Mathematics, 268
  identifier: 9781461479246
  identifier: http://dx.doi.org/10.1007/978-1-4614-7924-6
  record info:
    record creation date: 130920
    record change date: 20151029231528.0
    record identifier: 978-1-4614-7924-6