On the Unique Continuation along Curves of Germs of Solutions to Linear Differential Equations with Constant Coefficients

摘要

The unique analytic continuation property can be stated in terms of germs of functions as follows. If two analytic functions defined on an open set in the complex plane have the same germs at some point of a continuous curve contained in this set, then the germs of these functions are equal at all points of the curve. This note is devoted to a generalization of this fact to generalized solutions (in the sense of distributions) of linear partial differential equations with constant coefficients. It supplements results of the author's previous papers [ 1 ]-[5]. The uniqueness of continuation of solutions along curves implies the local uniqueness of a solution of the Cauchy problem. A survey of basic results on the local uniqueness of continuation of solutions to isotropic differential equations can be found in the monographs [6] by Hormander and [7] by Egorov.