Convolution of exp(-a*norm(x)^2) and exp(-b*norm(x)^2) ?

[jefferson_lc]

How do I compute convolution of exp(-a*norm(x)^2) and exp(-b*norm(x)^2) where a,b > 0 and x belongs to Rn?

I wonder if there is an easy way to compute this convolution using Fourier transform.

 

[Petr Mugver]

The convolution becomes simple multiplication after Fourier transforming. The two functions you have are gaussian functions, their FT is still a gaussian function, so is the product, and finally so is the antitransform. All you need is the formula for gaussian transforms.