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The Stationary Phase Method for Certain Degenerate Critical Points I

Published online by Cambridge University Press:  20 November 2018

Milos Dostal  and
Bernard Gaveau
Milos Dostal
Affiliation:
Stevens Institute of Technology, Hoboken, New Jersey
Bernard Gaveau
Affiliation:
Université Pierre et Marie Curie, Paris, France
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We consider, in this work, the asymptotic behaviour for large λ, of a Fourier integral

where 𝜑(x) is in general a C∞ function and a(x) a C∞ function with compact support. It is well known that the asymptotic behaviour of this integral is controlled by the behaviour of 𝜑 at its critical points (i.e., points where 𝜕𝜑/𝜕xj(x) = 0) and is given by local contributions at these points ([1], [3], [7], [9]).

In general, one assumes the hypothesis of non degenerate isolated critical point, namely that the determinant of the second derivative at the critical point is non zero.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 907 - 931
Copyright
Copyright © Canadian Mathematical Society 1989

References

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