## Remarks on Solvability of Pseudodifferential Operators in the Space of Hyperfunctions

J. Math. Sci. Univ. Tokyo
Vol. 13 (2006), No. 4, Page 595--616.

WAKABAYASHI, Seiichiro
Remarks on Solvability of Pseudodifferential Operators in the Space of Hyperfunctions
Let $X$ be an open subset, and let $p(x,\xi )$ be a pseudo-analytic symbol defined in $X\times \Bbb R^n$. Let $U$ and $V$ be open subsets of $X$ satisfying $U\Subset V\Subset X$. In this paper we prove that $p(x,D)$: $\as '(\overline{V})\to \bs (U)$ is surjective under some conditions on propagation of analyticity for the transposed operator $({}^tp)(x,D)$ of $p(x,D)$. This result was proved for differential operators by Cordaro and Tr\' epreau \cite{CT}.