Asymptotic Expansions of Integral Transforms with Oscillatory Kernels: A Generalization of the Method of Stationary Phase

Abstract

Integrals with integrands of the form H (lambda phi(t)) f(t) are considered for lambda to infinity and H(t) oscillatory for large argument. It is shown that the set of critical points for such integrals includes zeros of the phase function phi as well as all of those that arise in the analysis of the standard integrals of Fourier type; i.e., for the special case where H(t) = EXP(it). The contribution to the asymptotic expansion from each type of critical point is derived. In particular, a formula is obtained which generalizes the stationary phase formula associated with Fourier type integrals.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1971
Accession Number
AD0735785

Entities

People

  • N. Bleistein
  • R. A. Handelsman

Organizations

  • Denver Research Institute

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Asymptotic Series
  • Blood Coagulation Factors
  • Boundary Layer
  • Hypotheses
  • Integral Transforms
  • Integrals
  • Kernel Functions
  • Mathematics
  • Meromorphic Functions
  • Numbers
  • Real Numbers
  • Scientific Research
  • Sequences
  • Standards
  • Stationary

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Approximation Theory.
  • Linear Algebra