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: Probability on Compact Lie Groups
  name:
    name part: Applebaum, David.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2014
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXVI, 217 p. online resource.
  abstract: Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, stochastic analysis and harmonic analysis on groups. It will also be of interest to mathematicians working in Lie theory and physicists, statisticians and engineers who are working on related applications. A background in first year graduate level measure theoretic probability and functional analysis is essential; a background in Lie groups and representation theory is certainly helpful but the first two chapters also offer orientation in these subjects.
  table of contents: Introduction -- 1.Lie Groups -- 2.Representations, Peter-Weyl Theory and Weights -- 3.Analysis on Compact Lie Groups -- 4.Probability Measures on Compact Lie Groups -- 5.Convolution Semigroups of Measures -- 6.Deconvolution Density Estimation -- Appendices -- Index -- Bibliography.
  note: by David Applebaum.
  subject:
    topic: Mathematics
  subject:
    topic: Topological groups
  subject:
    topic: Lie groups
  subject:
    topic: Harmonic analysis
  subject:
    topic: Fourier analysis
  subject:
    topic: Functional analysis
  subject:
    topic: Probabilities
  subject:
    topic: Mathematics
  subject:
    topic: Probability Theory and Stochastic Processes
  subject:
    topic: Abstract Harmonic Analysis
  subject:
    topic: Topological Groups, Lie Groups
  subject:
    topic: Functional Analysis
  subject:
    topic: Fourier Analysis
  classification: QA273.A1-274.9
  classification: QA274-274.9
  classification: 519.2
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Probability Theory and Stochastic Modelling, 70
  identifier: 9783319078427
  identifier: http://dx.doi.org/10.1007/978-3-319-07842-7
  record info:
    record creation date: 140626
    record change date: 20151204175218.0
    record identifier: 978-3-319-07842-7