For specific systems of elliptic partial differential equations and the associated systems of formally hyperbolic equations in complex variables the solutions can be given using certain differential operators. These operators map holomorphic functions into the set of solutions of the system. In this article we consider the relation between a solution and the holomorphic functions generating it. In particular we determine the generators of the zero solution. Finally we give a general representation theorem for the solutions defined in the neighbourhood of an isolated singularity.
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Peter Berglez, Zur Darstellung von Lösungen bei Systemen partieller Differentialgleichungen, insbesondere be! isolierten Singularitäten. Z. Anal. Anwend. 10 (1991), no. 4, pp. 479–492DOI 10.4171/ZAA/469