# Division of distributions by polynomials.

I'm trying to solve the equation

$(1-|x|^2)T = 0$, where $T$ is a tempered distribution. I know how to do this (it is a common exercise) in dimension $1$. How can I solve it in higher dimensions?

Thank you very much.

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The solution is the direct product of $\delta(|x|-1)$ and any distribution on the sphere.