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Asymptotic Expansion of Fresnel Integrals Relative to a Non-Singular Quadratic Form

  • Ph. Blanchard
Conference paper

Abstract

We give an exposition of some of the methods of the mathematical theory of oscillatory integrals in infinitely many dimensions. In particular for a class of phase functions we extend the method of stationary phase and the corresponding asymptotic expansions to the infinite dimensional case.

Keywords

Asymptotic Expansion Oscillatory Integral Finite Dimensional Case Schrodinger Operator Real Separable Hilbert Space 
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References

  1. [1]
    S. Albeverio, R. Høegh-Krohn: “Mathematical theory of Feyn- man path integrals”, Lecture Notes in Math. 523. Berlin- Heidelberg-New York: Springer (1976).Google Scholar
  2. [2]
    S. Albeverio, R. Høegh-Krohn: “Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum iiiechan-ics”, Inventiones math. 40, 59–106 (1977).CrossRefMATHADSGoogle Scholar
  3. [3]
    S. Albeverio, Ph. Blanchard, R. Høegh-Krohn: “Oscillatory integrals and the method of stationary phase in infinitely many dimensions II”, Preprint 1980.Google Scholar
  4. [4]
    S. Albeverio, Ph. Blanchard, R. Høegh-Krohn: “The Poisson formula and the ζ-funetion for the Schrödinger Operators. ” Preprint 1980.Google Scholar

Copyright information

© Springer-Verlag/Wien 1980

Authors and Affiliations

  • Ph. Blanchard
    • 1
  1. 1.Fakultät für PhysikUniversität BielefeldFederal Republic of Germany

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