Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
    
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

1 Answer 1

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

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.