Extension of Solutions of Systems of Linear Differential Equations

The purpose of this paper is to prove some theorems on the extensibility of hyperfunction solutions and real analytic solutions of systems of linear differential equations with real analytic coefficients. It is Ehrenpreis [2] that revealed the intimate relations between the algebraic character of "overdetermin ed" systems of linear differential equations and Hartogs' theorem on the removable singularity of holomorphic functions of several complex variables. In fact, the essential part of his results can be summarized as follows: if a (generalized) function satisfies an "overdetermin ed" system of linear differential equations with constant coefficients outside a compact set in Rn, then it must be extended uniquely all over Rn as a solution of the same system. Note that the notion of "overdetermin ed" system is purely algebraic and that the Cauchy-Riemann equation, which holomorphic functions of n complex