On the uniqueness of generalized solutions of systems of differential equations with constant coefficients

This paper studies the problem of uniqueness of extension of generalized solutions of systems of partial differential equations with constant coefficients. Holmgren, I. M. Gelfand, G. E. Shilov, V. P. Palamodov, and other mathemati- cians dealt with the problem of extending the uniqueness of solutions of such systems. The problem of uniqueness of the Cauchy problem for evolutionary type with constant coefficients is also studied in I. M. Gelfand and G. E Shilov’s book. V. P. Palamodov investigated the uniqueness problem and established more precise theorems on the possibility of extending generalized solutions given in a neighborhood of the boundary of the domain in the most important situations. Uniqueness problems similar to the Goursat problem were investigated by A. M. Berdimuratov. This paper is devoted to the following problem: under what conditions is any generalized solution of infinite order of a system of partial differential equations with constant coefficients defined in a neighborhood of three adjacent faces of a parallelepiped in, can be uniquely extended to some of its neighborhood.