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.

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

If $u \in \mathcal D'(\mathbb R^n)$, $u$ is homogeneous of degree $0$ and rotational invariant, it is necessarily that $u$ is a constant? (Since if $u \in C^\infty$, the conclusion obviously hold.)

share|cite|improve this question
Could you state your definition of homogeneous distribution? I assume it is rolled down to the test function, but I would ask for your specification. – Vobo Apr 23 '12 at 20:22

Any homogeneous distribution u of degree a in $\mathbb{R}^{n}$ can be writen as the form $$u=r^{a}f$$ where $r=|x|$,and $f\in\mathcal D'(S^{n-1})$.So,in your case, distributions on the unit sphere which is symmetric will satisfy. see aslo

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.