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Gaussians Closed under Convolution

In §D.8 we show that

  • the Fourier transform of a Gaussian is Gaussian, and in §D.2 that
  • the product of any two Gaussians is Gaussian.
Therefore, it follows from the convolution theorem for Fourier transforms (§B.7) that the convolution of any two Gaussians is Gaussian.

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Gaussians Closed under Multiplication