Asymptotic approximation of degenerate fiber integrals

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:320

Article

Camus, Brice

关键词: asymptotics;    fiber integrals;    degenerate oscillatory integrals;   

DOI  :  10.1016/j.jmaa.2005.07.046

来源: Elsevier

【 摘 要 】

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. (C) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

Free