Let $f$ and $g$ be distributions on $\mathbb{R}$ with compact support. Do we have
$\inf (\textrm{supp}(f*g)) = \inf (\textrm{supp}(f)) + \inf (\textrm{supp}(g))$
Where 'supp' denotes de the support of a distribution ?
The left term is obviously greater than the right one. But the other inequality seems trickier to me (I guess it's always easier to prove that things are equal to zero). Any help in finding either a counterexample, proof, or reference for that statement would be appreciated. Thanks.