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well, i have to prove that the inv. fourier transform of a gaussian (e^(-(k^2/2)) is a gaussian, i know some elementary complex analysis(never actually taken a class in it), not well enough, it seems, to find the solution to this. I tried to integrate over a circular contour, and let the radius of the circle go to infinity, i couldn't solve the integral that i obtained (it was pretty complicated). Also, i don't quite understand this, the integrand is complex analytic everywhere, so if i integrate it over a circular contour, wouldn't i get 0, by cauchy's theorem?
Any help much appreciated
Any help much appreciated