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 Mremainder is proved for the Dirac 8-function. The analyticitycondition of Jones and Kline is now replaced by infinite differentiability. Connections with the asymptotic expansions of Jeanquartier and Malgrange are also discussed. © 1981 American Mathematical Society.
| Original language | English |
|---|---|
| Pages (from-to) | 509-521 |
| Journal | Mathematics of Computation |
| Volume | 37 |
| Issue number | 156 |
| DOIs | |
| Publication status | Published - Oct 1981 |
| Externally published | Yes |
Research Keywords
- Asymptotic expansion
- Dirac 5-function
- Multi-dimensional stationary-phase approximation
- Surface distribution
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