Geodesic
Asymptotic Expansion of a Class of Multi-Dimensional Integrals
Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 1079-1090

Voir la notice de l'article provenant de la source Cambridge University Press

The aim of this paper is to derive the expansion of the following class of multi-dimensional integrals with respect to the large parameter λ when Ω is a subset of Rn , a > 0, w is a strictly positive and bounded function on Σ and fp means an integration in the finite part sense of Hadamard (see Section 2). This is performed for weak assumptions bearing on pseudofunction K and by extending to higher dimensional cases the tools developed in the one-dimensional context. The range of applications of the proposed results is outlined by the exhibition of several examples.
DOI : 10.4153/CJM-1996-056-7
Mots-clés : 41A60, 41A60 
Sellier, A. Asymptotic Expansion of a Class of Multi-Dimensional Integrals. Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 1079-1090. doi: 10.4153/CJM-1996-056-7
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[1] 1. Barlet, P., Développement asymptotique des fonctions obtenues sur les fibres, Invent., Math 68(1982), 129–174. Google Scholar

[2] 2. Bleistein, N. and Handelsman, R.A., Asymptotic Expansions of Integrals, Holt, Rinehart and Winston, New York, 1975. Google Scholar

[3] 3. Bruning, J., On the asymptotic expansion of some integrals, Arch., Math. 42(1984), 253–259. Google Scholar

[4] 4. Estrada, R. and Kanwal, R.P., The asymptotic expansion of certain multi-dimensional generalized functions, J. Math. Anal., Appl. 163(1992), 264–283. Google Scholar

[5] 5. Estrada, R., Asymptotic Analysis, A distributional Approach, Boston, Birkhauser, 1994. Google Scholar

[6] 6. Hadamard, J., Lectures on Cauchy's problem in linear differential equations, New York, Dover, 1932. Google Scholar

[7] 7. Malgrange, B., Integrales asymptotiques et monodromie, Ann. Sci. Ecole Norm. Sup., (4) 7(1974), 405- 430. Google Scholar

[8] 8. McClure, J.P. and Wong, R., Asymptotic expansion of a multiple integral, SIAM.J. Math., Anal. 18(1987), 1630–1637. Google Scholar

[9] 9. Schwartz, L., Theorie des Distributions, Paris, Hermann, 1966. Google Scholar

[10] 10. Sellier, A., Asymptotic expansions of a class of Integrals, Proc. Roy. Soc. London Ser., A 445(1994), 693–710. Google Scholar

[11] 11. Sellier, A., An alternative Method for the Asymptotic expansion of a double integral, J. Math. Anal., Appl. 194(1995), 741–762. Google Scholar

[12] 12. Wong, R., Asymptotic Approximations of Integrals, Boston, Academic Press, 1989. Google Scholar

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