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Justification of the Stationary Phase Approximation in Time-Domain Asymptotics

J. P. McClure and R. Wong
Proceedings: Mathematical, Physical and Engineering Sciences
Vol. 453, No. 1960 (May 8, 1997), pp. 1019-1031
Published by: Royal Society
Stable URL: http://www.jstor.org/stable/53112
Page Count: 13
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Justification of the Stationary Phase Approximation in Time-Domain Asymptotics
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Abstract

A rigorous proof is supplied for the validity of an asymptotic approximation to the integral I(λ )=∫ab g(x)p{λ f(x)} dx, where f(x) and g(x) are sufficiently smooth functions on [a, b] and p(x) is a piece-wise smooth periodic function with mean zero. In addition, a two-dimensional generalization is given. Problems concerning coalescence of two stationary points and a stationary point near an end point are also considered.

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