Geodesic
The application of an interpolational method
Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 735-752.

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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]. 
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     author = {A. F. Leont'ev},
     title = {The application of an interpolational method},
     journal = {Matemati\v{c}eskie zametki},
     pages = {735--752},
     publisher = {mathdoc},
     volume = {18},
     number = {5},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a10/}
}
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A. F. Leont'ev. The application of an interpolational method. Matematičeskie zametki, Tome 18 (1975) no. 5, pp. 735-752. http://geodesic.mathdoc.fr/item/MZM_1975_18_5_a10/