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: Distributions
    sub title: Theory and Applications
  name:
    name part: Duistermaat, J.J.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: Kolk, J.A.C.
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2010
    edition: 1.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XVI, 445 p. 41 illus. online resource.
  abstract: This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. Throughout the book, methods are developed to deal with formal calculations involving functions, series, and integrals that cannot be mathematically justified within the classical framework. Key features: • Many examples, exercises, hints, and solutions guide the reader throughout the text. • Includes an introduction to distributions, differentiation, convergence, convolution, the Fourier transform, and spaces of distributions having special properties. • Original proofs, which may be difficult to locate elsewhere, are given for many well-known results. • The Fourier transform is transparently treated and applied to provide a new proof of the Kernel Theorem, which in turn is used to efficiently derive numerous important results. • The systematic use of pullback and pushforward introduces concise notation. • Emphasizes the role of symmetry in obtaining short arguments and investigates distributions that are invariant under the actions of various groups of transformations. Distributions: Theory and Applications is aimed at advanced undergraduates and graduate students in mathematics, theoretical physics, and engineering, who will find this textbook a welcome introduction to the subject, requiring only a minimal mathematical background. The work may also serve as an excellent self-study guide for researchers who use distributions in various fields.
  table of contents: Motivation -- Test Functions -- Distributions -- Differentiation of Distributions -- Convergence of Distributions -- Taylor Expansion in Several Variables -- Localization -- Distributions with Compact Support -- Multiplication by Functions -- Transposition: Pullback and Pushforward -- Convolution of Distributions -- Fundamental Solutions -- Fractional Integration and Differentiation -- Fourier Transform -- Distribution Kernels -- Fourier Series -- Fundamental Solutions and Fourier Transform -- Supports and Fourier Transform -- Sobolev Spaces -- Appendix: Integration -- Solutions to Selected Problems.
  note: by J.J. Duistermaat, J.A.C. Kolk.
  subject:
    topic: Mathematics
  subject:
    topic: Approximation theory
  subject:
    topic: Fourier analysis
  subject:
    topic: Functional analysis
  subject:
    topic: Differential equations
  subject:
    topic: Partial differential equations
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Mathematics
  subject:
    topic: Functional Analysis
  subject:
    topic: Approximations and Expansions
  subject:
    topic: Applications of Mathematics
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Fourier Analysis
  subject:
    topic: Ordinary Differential Equations
  classification: QA319-329.9
  classification: 515.7
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Cornerstones
  identifier: 9780817646752
  identifier: http://dx.doi.org/10.1007/978-0-8176-4675-2
  record info:
    record creation date: 100806
    record change date: 20151204182208.0
    record identifier: 978-0-8176-4675-2