Singularities in Fuchsian Cauchy Problems with Holomorphic Data

Abstract

It has been proved by Baouendi and Goulaouic that the holomorphic Cauchy problem for a Fuchsian partial differential operator of weight $m-m^{\prime }$ has a unique solution if its characteristic exponents avoid integers $\ge m-m^{\prime }$. In the present paper we consider the singularity of the solution which appears if some of the characteristic exponents take integral values $\ge m-m^{\prime }$.