Holomorphic extension of fundamental solutions of elliptic linear partial differential operators of higher order with analytic coefficients

We prove that every fundamental solution of an elliptic linear partial differential operator with analytic coefficients in Ω   open subset of RnRn and simple complex characteristics can be holomorphically continued at least locally as a multi-valued analytic function x⟶E(x,y)x⟶E(x,y) in CnCn up to the complex bicharacteristic conoid. This holomorphic extension is ramified around the bicharacteristic conoid and belongs to the Nilsson class.