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On a method of asymptotic evaluation of multiple integrals


Authors: R. Wong and J. P. McClure
Journal: Math. Comp. 37 (1981), 509-521
MSC: Primary 41A60; Secondary 41A63
DOI: https://doi.org/10.1090/S0025-5718-1981-0628712-1
Remarks: Math. Comp. 45, no. 171 (1969), pp. 197-198.
MathSciNet review: 628712
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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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DOI: https://doi.org/10.1090/S0025-5718-1981-0628712-1
Keywords: Asymptotic expansion, multi-dimensional stationary-phase approximation, Dirac $ \delta $-function, surface distribution
Article copyright: © Copyright 1981 American Mathematical Society