Removable singularities of holomorphic solutions of linear partial differential equations

Abstract

In a complex domain V⊂ \bm{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\backslash K has a holomorphic extension in V. Besides, it is applied to the propagation of singularities for equations with non-involutive double characteristics.