The application of an interpolational method

We consider an equation of infinite order in generalized derivatives in the sense of A. O. Gel'fond with a characteristic function of finite order $L(\lambda)=L_1(\lambda)\dots L_n(\lambda)$. It is explained by a purely analytical method (by the application of an interpolational method) when any solution of the equation is the sum of the solutions of similar equations with the characteristic functions $L_1(\lambda)\dots L_n(\lambda)$. In the case of an equation in ordinary derivatives, when $L(\lambda)$ is a function of exponential type, the problem is solved by the application of algebraic and functional methods of V. V. Napalkov [1].