ASYMPTOTIC-EXPANSION OF A CLASS OF MULTIDIMENSIONAL INTEGRALS

The aim of this paper is to derive the expansion of the following clas s of multi-dimensional integrals I(lambda) := fp integral(Omega)K[x.la mbda w(theta)r(a)] dx. with respect to the large parameter lambda when Omega is a subset of R(n), a > 0, w is a strictly positive and bounde d function on Sigma and fp means an integration in the finite part sen se of Hadamard (see Section 2). This is performed for weak assumptions bearing on pseudofunction K and by extending to higher dimensional ca ses the tools developed in the one-dimensional context. The range of a pplications of the proposed results is outlined by the exhibition of s everal examples.