we have these 2 functons:

H(u)= A*e^[(-u^2)/2*sigma^2)]
h(x)= sqrt(2pi)*sigma*A*e^[-2*(pi^2)*(sigma^2)*(x^2)]

and also we have Fourier transforms.

question: prove that H(u) is a transform of h(x), or h(x) is a transform of H(u).