# Gaussian Kernel =?= linear combination of infinite number of Gaussian distributions?

From the literature we know a Gaussian Kernel/RBF has a corresponding Hilbert space with infinite number of dimensions.

Now my question is, specially in the context of a Gaussian Process, can I consider a Gaussian kernel as a linear combination of infinite number of Gaussian distributions?

I'm almost certain that's the case, but I can't find the right reference for it.

• "consider a Gaussian kernel as a linear combination of infinite number of Gaussian distributions" Wouldn't this statement imply that a Gaussian mixture in general can be summarized exactly into one Gaussian distribution? Does not sound right to me. – wij Jul 7 '17 at 11:12
• No, Gaussian functions are closed under summation only if they all have the same mean, otherwise adding two gaussian functions with different means wouldn't give you a single gaussian function. – adrin Jul 8 '17 at 14:44