Removable singularities of holomorphic solutions of linear partial differential equations

Abstract

In a complex domain $V\subset C^n$, let $P$ be a linear holomorphic partial differential operator and $K$ be its characteristic hypersurface. When the localization of $P$ at $K$ is a Fuchsian operator having a non-negative integral characteristic index, it is proved, under some conditions, that every holomorphic solution to $Pu=0$ in $V\setminus K$ has a holomorphic extension in $V$. Besides, it is applied to the propagation of singularities for equations with non-involutive double characteristics.