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: Functions of Bounded Variation and Their Fourier Transforms
  name:
    name part: Liflyand, Elijah.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2019
    edition: 1st ed. 2019.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXIV, 194 p. online resource.
  abstract: Functions of bounded variation represent an important class of functions. Studying their Fourier transforms is a valuable means of revealing their analytic properties. Moreover, it brings to light new interrelations between these functions and the real Hardy space and, correspondingly, between the Fourier transform and the Hilbert transform. This book is divided into two major parts, the first of which addresses several aspects of the behavior of the Fourier transform of a function of bounded variation in dimension one. In turn, the second part examines the Fourier transforms of multivariate functions with bounded Hardy variation. The results obtained are subsequently applicable to problems in approximation theory, summability of the Fourier series and integrability of trigonometric series. .
  table of contents: Stock and tools -- Functions with derivative in a Hardy space -- Integrability spaces: wide, wider and widest -- Sharper results -- Stock and tools for several dimensions -- Integrability of the Fourier transforms -- Sharp results -- Bounded variation and discretization -- Multidimensional case: radial functions.
  note: by Elijah Liflyand.
  subject:
    topic: Harmonic analysis
  subject:
    topic: Abstract Harmonic Analysis
  classification: QA403-403.3
  classification: 515.785
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Applied and Numerical Harmonic Analysis
  identifier: 9783030044299
  identifier: https://doi.org/10.1007/978-3-030-04429-9
  record info:
    record creation date: 190306
    record change date: 20190618151525.0
    record identifier: 978-3-030-04429-9