0
$\begingroup$

Let $G$ be a finitely generated dense subgroup of $\mathbb{R}^n$, and $f$ be a character on $G$.

In the situation I'm looking at $f$ is either $1$ or $-1$ at any point.

Function $f$ can be extended to $\mathbb{R}^n$ by setting it to $0$ outside $G$. Is there any way to associate a distribution to $f$? For example one could try to form an infinite sum of Diracs on $G$, or perhaps a limit of suitably normalized finite sums of Diracs? Or maybe it can't be done in a meaningful way?

Any idea, reference or comment on how to deal with such objects is welcome.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.