Originally Posted by

**davidmccormick** f(x) = e^-(x^2) and g(x) = e^-2(x^2).

Compute f*g (their convolution). Use it to show that if

h_t(x) = 1/(4 \pi t) e^{(-x^2)/4t}

we have h_t * h_s = h_(t+s)

My first thought was to take the Fourier transform of f and g - these are standard for example f^(k) = sqrt(\pi) e^{-(\pi ^2) k^2} - then use the property for the convolution of Fourier transform, namely (f*g)^(k) = f^(k) g^(k), but to no avail. Alternatively, I can't evaluate the integral when using the definition of convolution.