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Apr 16, 2010 at 11:07 comment added Deane Yang Well, they're not smooth distributions. But they're not just measures, either, because if $x_0 \in U$, the dual space contains the functional $f \mapsto \langle A,\partial_i\partial_jf(x_0)\rangle$, where $A \in Sym^*$.
Apr 16, 2010 at 2:37 comment added Yemon Choi Since $U$ is compact and we're dealing with a fixed degree of differentiability, I don't think we get distributions per se. My guess would be `$Sym*$'-valued complex measures on $U$.
Apr 16, 2010 at 1:51 history answered Deane Yang CC BY-SA 2.5