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.)
Homogeneous and rotational invariant distribution
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analysis
functional-analysis
distribution-theory
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0Could you state your definition of homogeneous distribution? I assume it is rolled down to the test function, but I would ask for your specification. – 2012-04-23