On a method of asymptotic evaluation of multiple integrals

Wong, R.; McClure, J. P.

doi:10.1090/S0025-5718-1981-0628712-1

On a method of asymptotic evaluation of multiple integrals
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by R. Wong and J. P. McClure PDF

Math. Comp. 37 (1981), 509-521 Request permission

Abstract:

In this paper, some of the formal arguments given by Jones and Kline [J. Math. Phys., v. 37, 1958, pp. 1-28] are made rigorous. In particular, the reduction procedure of a multiple oscillatory integral to a one-dimensional Fourier transform is justified, and a Taylor-type theorem with remainder is proved for the Dirac $\delta$-function. The analyticity condition of Jones and Kline is now replaced by infinite differentiability. Connections with the asymptotic expansions of Jeanquartier and Malgrange are also discussed.

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Distributions on Surfaces