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Asymptotic expansion of double Laplace-type integrals: The case of non-stationary minimum points


Authors: Nesrine Kamouche and Abdallah Benaissa
Journal: Proc. Amer. Math. Soc. 144 (2016), 3741-3756
MSC (2010): Primary 41A60; Secondary 53A04
DOI: https://doi.org/10.1090/proc/13064
Published electronically: May 4, 2016
MathSciNet review: 3513535
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Abstract: In this paper, we show that the asymptotic expansion of a double Laplace-type integral with a non-stationary minimum point, located on the boundary of the domain of integration, is governed by the order of contact between the boundary curve and the level curve of the phase through the minimum point. This achievement will enable us to construct complete asymptotic expansions in more general settings. Especially, the problem will be completely solved if the phase and the boundary curve of the domain of integration are analytic near the minimum point.


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Additional Information

Nesrine Kamouche
Affiliation: Laboratoire LAMIE, UHL University, 05000 Batna, Algeria
Email: kamouche_nesrine@hotmail.fr

Abdallah Benaissa
Affiliation: Laboratoire LAMIE, UHL University, 05000 Batna, Algeria
Email: benaissa.abdallah@yahoo.fr

DOI: https://doi.org/10.1090/proc/13064
Keywords: Asymptotic expansion, Laplace-type integral, boundary minimum point.
Received by editor(s): April 2, 2015
Received by editor(s) in revised form: September 21, 2015
Published electronically: May 4, 2016
Communicated by: Walter Van Assche
Article copyright: © Copyright 2016 American Mathematical Society