## ProblÃ¨me de Cauchy CaractÃ©ristique Ã  Solution EntiÃ¨re

J. Math. Sci. Univ. Tokyo
Vol. 8 (2001), No. 1, Page 89--105.

For a Fuchsian differential operator with order $m$ and weight $p\in[0,m]$ in the sense of M. S. Baouendi and C. Goulaouic, we approach the study of the Cauchy problem in entire functions spaces. This article is mainly based on the fixed-point theorem in a Banach space defined by a majorant function with two variables that is suitable to this kind of operator. The proposed method allows one to generalize a H. Yamane theorem and to give the order of the solution ; when $p=m$, we find again the well-known theorems.