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