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How to compute the convolution of two functions which diverge at infinity?

e.g. $e^{x^2}*e^{x^4}$

We can't directly write as $\int_{-\infty}^\infty e^{t^2}e^{(x-t)^4}~dt$ or $\int_{-\infty}^\infty e^{(x-t)^2}e^{t^4}~dt$ as both integrals are divergent.

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1. View the two functions as distributions,. 2. Compute their Fourier transforms. These are also distributions. 3. Try to multiply them. If you can't, you're out of luck. – Hans Engler Nov 1 '12 at 19:53

It's not a matter of "computing": the question is, what do you mean by "convolution" in a case such as this?

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