## Remarks on Analytic Hypoellipticity and Local Solvability in the Space of Hyperfunctions

J. Math. Sci. Univ. Tokyo
Vol. 10 (2003), No. 1, Page 89--117.

Wakabayashi, Seiichiro
Remarks on Analytic Hypoellipticity and Local Solvability in the Space of Hyperfunctions
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Abstract:
Let $p(x,D)$ be a pseudodifferential operator on $\Bbb R^n$ with a ( formal) analytic symbol $p(x,Î¾ )$, and let $x^0\in \Bbb R^n$. In this paper we prove that the transposed operator ${}^tp(x,D)$ of $p(x,D)$ is locally solvable at $x^0$ modulo analytic functions in the space of hyperfunctions if $p(x,D)$ is analytic hypoelliptic at $x^0$. We also microlocalize this result.

Mathematics Subject Classification (2000): Primary 35G05; Secondary 35A07, 35H10, 35A20
Mathematical Reviews Number: MR1963799

Received: 2002-06-03