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: Singularities of integrals
    sub title: Homology, hyperfunctions and microlocal analysis
  name:
    name part: Pham, Frédéric.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxk
    date issued: 2011
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XI, 217 p. online resource.
  abstract: Bringing together two fundamental texts from Frédéric Pham’s research on singular integrals, the first part of this book focuses on topological and geometrical aspects while the second explains the analytic approach. Using notions developed by J. Leray in the calculus of residues in several variables and R. Thom’s isotopy theorems, Frédéric Pham’s foundational study of the singularities of integrals lies at the interface between analysis and algebraic geometry, culminating in the Picard-Lefschetz formulae. These mathematical structures, enriched by the work of Nilsson, are then approached using methods from the theory of differential equations and generalized from the point of view of hyperfunction theory and microlocal analysis. Providing a ‘must-have’ introduction to the singularities of integrals, a number of supplementary references also offer a convenient guide to the subjects covered. This book will appeal to both mathematicians and physicists with an interest in the area of singularities of integrals. Frédéric Pham, now retired, was Professor at the University of Nice. He has published several educational and research texts. His recent work concerns semi-classical analysis and resurgent functions.
  table of contents: Differentiable manifolds -- Homology and cohomology of manifolds -- Leray’s theory of residues -- Thom’s isotopy theorem -- Ramification around Landau varieties -- Analyticity of an integral depending on a parameter -- Ramification of an integral whose integrand is itself ramified -- Functions of a complex variable in the Nilsson class -- Functions in the Nilsson class on a complex analytic manifold -- Analyticity of integrals depending on parameters -- Sketch of a proof of Nilsson’s theorem -- Examples: how to analyze integrals with singular integrands -- Hyperfunctions in one variable, hyperfunctions in the Nilsson class -- Introduction to Sato’s microlocal analysis.
  note: by Frédéric Pham.
  subject:
    topic: Mathematics
  subject:
    topic: Algebraic geometry
  subject:
    topic: Approximation theory
  subject:
    topic: Functions of complex variables
  subject:
    topic: Mathematics
  subject:
    topic: Several Complex Variables and Analytic Spaces
  subject:
    topic: Algebraic Geometry
  subject:
    topic: Approximations and Expansions
  classification: QA331.7
  classification: 515.94
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Universitext
  identifier: 9780857296030
  identifier: http://dx.doi.org/10.1007/978-0-85729-603-0
  record info:
    record creation date: 110422
    record change date: 20151125021722.0
    record identifier: 978-0-85729-603-0