Geodesic
A functional equation
Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 733-742 Cet article a éte moissonné depuis la source Math-Net.Ru

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The translational functional equation (1) with right-hand side analytic in a finite convex region $G$ is investigated. It is proved that a solution exists which is analytic in a finite convex region $G_1$ determined by $G$. A corollary of this result is the existence of analytic solutions of differential-difference equations of finite order and of difference equations of infinite order with constant coefficients. 
@article{MZM_1969_5_6_a10,
     author = {Yu. F. Korobeinik},
     title = {A~functional equation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {733--742},
     year = {1969},
     volume = {5},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a10/}
}
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Yu. F. Korobeinik. A functional equation. Matematičeskie zametki, Tome 5 (1969) no. 6, pp. 733-742. http://geodesic.mathdoc.fr/item/MZM_1969_5_6_a10/