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I have a problem, which is quite urgent, as I have only today discovered an error in a proof i had in a thesis which is to be handed in tomorrow. The problem, if stated in as full generality as ...

Let's denote the set of all Pseudo-differential operators with symbol of “order” $d$ by $\Psi_d(M)$ and Sobolev space on $M$ by $H_s(M)$. It is known that If $P\in\Psi_d(M)$ Then $P$ extends to a ...