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Cauchy problem in entire function spaces. (Problème de Cauchy caractéristique à solution entière.) (French) Zbl 0984.35004
Summary: For a Fuchsian differential operator with order \(m\) and weight \(p\in[0,m]\) in the sense of M. S. Baouendi and C. Goulaouic [Commun. Pure Appl. Math. 26, 455-475 (1973; Zbl 0256.35050)], 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.

35A10 Cauchy-Kovalevskaya theorems
35A20 Analyticity in context of PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)