# Time-domain asymptotics and the method of stationary phase

@article{Chapman1992TimedomainAA, title={Time-domain asymptotics and the method of stationary phase}, author={Craig J. Chapman}, journal={Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences}, year={1992}, volume={437}, pages={25 - 40} }

A technique is described for obtaining the asymptotic behaviour at large λ of integrals having the form I(λ) = ∫ g(x) p{λf(x)} dx, where p is an arbitrary periodic function with mean zero. It is based on the fact that the method of stationary phase may be applied directly to p{λf(x)}, without decomposition of p into Fourier components: thus a simple minimum of f at x = x0 gives a term containing a fractional integral of order one-half, proportional to p̂+(y) = {∞y{p(x)/ (x — y)1/2} dx evaluated… CONTINUE READING

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