Asymptotic approximation of degenerate fiber integrals

Details Asymptotic approximation of degenerate fiber integrals Asymptotic approximation of degenerate fiber integrals

2005-03-23

arxiv.org/abs/math/0503505v1

Journal of Mathematical Analysis and Applications. Volume 320, Issue 2 , 15 August 2006, Pages 528-542

Mathematics

General Mathematics

22 pages, perhaps to be revised

Scientific paper

10.1016/j.jmaa.2005.07.046

We study asymptotics of fiber integrals depending on a large parameter. When the critical fiber is singular, full-asymptotic expansions are established in two different cases : local extremum and isolated real principal type singularities. The main coefficients are computed and invariantly expressed. In the most singular cases it is shown that the leading term of the expansion is related to invariant measures on the spherical blow-up of the singularity. The results can be applied to certain degenerate oscillatory integrals which occur in spectral analysis and quantum mechanics.

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