Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let $$f(x)=\sum_{s=-\infty}^{\infty}e^{-2\pi ixsk}$$ $k$ integer. Does this integral exist? $$\int_{0}^{1}(f(x))^{2}dx$$

share|cite|improve this question
Have you tried proving continuity of $f^2$? – Mose Wintner Apr 23 '11 at 15:26
up vote 3 down vote accepted

I think the problem is, to have a meaning for $f(x)^2$, having in mind that the "Shah function" is merely a distribution (also known as Dirac comb). It is known that it is notoriously difficult to have a proper notion for the multiplication of distributions and I do not know a proper way of multiplying a $\delta$ with itself.

share|cite|improve this answer

Your Answer


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.