## Existence of Distribution Null-Solutions for Every Fuchsian Partial Differential Operator

J. Math. Sci. Univ. Tokyo
Vol. 5 (1998), No. 1, Page 1--18.

Mandai, Takeshi
Existence of Distribution Null-Solutions for Every Fuchsian Partial Differential Operator

Abstract:
We construct a distribution null-solution for {\em every} Fuchsian partial differential operator in the sense of Baouendi- Goulaouic with real-analytic coefficients, if the initial surface is characteristic. This construction is valid also for Fuchsian hyperbolic operators with $C^\infty$ coefficients considered by H. Tahara, and for some non-Fuchsian operators with real-analytic coefficients.

Mathematics Subject Classification (1991): Primary 35D05; Secondary 35A07, 35M99, 35L80
Mathematical Reviews Number: MR1617069