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

1. Aug 14, 2010

### 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.

2. Aug 14, 2010

### 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.

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