Timeline for The derivative of a non-tempered distribution can be tempered?

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Mar 18, 2014 at 14:18	comment	added	Thomas		I have a concern: that tells me that for any tempered distribution $T$, there is a tempered distribution solution to $\partial x_1...\partial x_d u=T$. In dimension $1$ the only primitives of $0$ are constants so in fact any solution of this equation is tempered. But what about in higher dimension? The solutions to $\partial x_1...\partial x_d u=0$ have support in the union of the axes of $\mathbb R^d$ but is there more?
Mar 18, 2014 at 13:55	vote	accept	Thomas
Mar 18, 2014 at 14:40
S Mar 18, 2014 at 13:40	history	suggested	coimbra	CC BY-SA 3.0	responded to OP's objection.
Mar 18, 2014 at 13:39	review	Suggested edits
S Mar 18, 2014 at 13:40
Mar 18, 2014 at 13:11	comment	added	Thomas		I agree that there is a structure theorem for tempered distributions. In fact $u=\partial^\alpha ((1+\|x\|^2)^n f(x))$ for some continuous and bounded function $f$ and multi-indexe $\alpha$ and integer $n$. The problem is if $\alpha=(\alpha_1,...,\alpha_d)$ is such that $\alpha_i=0$ for some $i$: then taking the derivative of a lower order makes no sense.
Mar 18, 2014 at 12:32	history	answered	barcelos	CC BY-SA 3.0