Asymptotic Expansions of Integral Transforms with Oscillatory Kernels: A Generalization of the Method of Stationary Phase
DENVER RESEARCH INST CO DIV OF MATHEMATICAL SCIENCES
Pagination or Media Count:
Integrals with integrands of the form H lambda phit ft are considered for lambda to infinity and Ht oscillatory for large argument. It is shown that the set of critical points for such integrals includes zeros of the phase function phi as well as all of those that arise in the analysis of the standard integrals of Fourier type i.e., for the special case where Ht EXPit. The contribution to the asymptotic expansion from each type of critical point is derived. In particular, a formula is obtained which generalizes the stationary phase formula associated with Fourier type integrals.
- Numerical Mathematics