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On a Method of Asymptotic Evaluation of Multiple Integrals
This research was partially supported by the Natural Sciences and Engineering Research Council of Canada under Grants A7359 and A8069.
https://doi.org/10.1142/9789814656054_0014Cited by:0 (Source: Crossref)
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 δ-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.
Keywords:
- Asymptotic expansion
- multi-dimensional stationary-phase approximation
- Dirac δ-function
- surface distribution
AMSC: Primary 41A60
