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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeNov 2nd 2017

started some minimum at convolution product of distributions

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeNov 28th 2017
• (edited Nov 28th 2017)

added this statement (here and also at wave front set here):

Let $u,v \in \mathcal{E}'(\mathbb{R}^n)$ be two compactly supported distributions. Then the wave front set of their convolution of distributions is

$WF(u \star v) \;=\; \left\{ (x + y, k) \;\vert\; (x,k) \in WF(u) \,\text{and}\, (y,k) \in WF(u) \right\} \,.$
1. I checked the hormander textbook, the definition contains an error, the function convoluted with the tempered distribution has to be smooth and with compact support.

Daniele Zerbini