Quantcast
Viewing all articles
Browse latest Browse all 9124

Fix distribution $u$, find a distribution $\tilde u$ satisfying $x\cdot\tilde u=u$

Prove that, for every distribution $u\in\mathcal D'(\mathbb R)$,there exists a distribution $\tilde u\in \mathcal D'(\mathbb R)$ satisfying $x\cdot\tilde u=u$.

It seems that it can be solved by Fourier Transform. But this is an exercise in the chapter which is before Fourier Transform. So can I solve this without fourier transform?

Maybe I can consider the support set of $u$, but I still cannot solve that.


Viewing all articles
Browse latest Browse all 9124

Trending Articles



<script src="https://jsc.adskeeper.com/r/s/rssing.com.1596347.js" async> </script>