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

  1. Aug 14, 2010 #1
    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. jcsd
  3. Aug 14, 2010 #2
    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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