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.
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References
S. Albeverio, R. Høegh-Krohn: “Mathematical theory of Feyn- man path integrals”, Lecture Notes in Math. 523. Berlin- Heidelberg-New York: Springer (1976).
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).
S. Albeverio, Ph. Blanchard, R. Høegh-Krohn: “Oscillatory integrals and the method of stationary phase in infinitely many dimensions II”, Preprint 1980.
S. Albeverio, Ph. Blanchard, R. Høegh-Krohn: “The Poisson formula and the ζ-funetion for the Schrödinger Operators. ” Preprint 1980.
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Blanchard, P. (1980). Asymptotic Expansion of Fresnel Integrals Relative to a Non-Singular Quadratic Form. In: Streit, L. (eds) Quantum Fields — Algebras, Processes. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8598-8_7
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DOI: https://doi.org/10.1007/978-3-7091-8598-8_7
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-8600-8
Online ISBN: 978-3-7091-8598-8
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