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: Symplectic Methods in Harmonic Analysis and in Mathematical Physics
  name:
    name part: Gosson, Maurice A. de.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: sz
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XXIV, 338 p. online resource.
  abstract: The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space is introduced and studied, where the main role is played by “Bopp operators” (also called “Landau operators” in the literature). This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
  note: by Maurice A. de Gosson.
  subject:
    topic: Mathematics
  subject:
    topic: Operator theory
  subject:
    topic: Partial differential equations
  subject:
    topic: Differential geometry
  subject:
    topic: Mathematical physics
  subject:
    topic: Mathematics
  subject:
    topic: Operator Theory
  subject:
    topic: Partial Differential Equations
  subject:
    topic: Mathematical Physics
  subject:
    topic: Differential Geometry
  classification: QA329-329.9
  classification: 515.724
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Pseudo-Differential Operators, Theory and Applications ; 7
  identifier: 9783764399924
  identifier: http://dx.doi.org/10.1007/978-3-7643-9992-4
  record info:
    record creation date: 110728
    record change date: 20151030021057.0
    record identifier: 978-3-7643-9992-4