Singularities in Fuchsian Cauchy problems with holomorphic data (Q5931087)

Summary: It has been proved by \textit{M. S. Baouendi} and \textit{C. Goulaouic} [Commun. Pure Appl. Math. 26, 455-475 (1973; Zbl 0264.35047)] that the holomorphic Cauchy problem for a Fuchsian partial differential operator of weight \(m-m'\) has a unique solution if its characteristic exponents avoid integers \(\geq m-m'\). In the present paper we consider the singularity of the solution which appears if some of the characteristic exponents take integral values \(\geq m-m'\).