Geodesic
Solvability of a convolution equation in convex domains
Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 787-796
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For an exponential function $a(z)$ we consider the convolution $a*x$ in the function space $H(G)$, consisting of functions analytic in convex domains $G$. We obtain conditions (close to necessary and sufficient) on $G$ and $G_1$ subject to which the equation $a*(H(G_1))=H(G)$ is satisfied. 
@article{MZM_1974_15_5_a15,
     author = {O. V. Epifanov},
     title = {Solvability of a~convolution equation in convex domains},
     journal = {Matemati\v{c}eskie zametki},
     pages = {787--796},
     year = {1974},
     volume = {15},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a15/}
}
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O. V. Epifanov. Solvability of a convolution equation in convex domains. Matematičeskie zametki, Tome 15 (1974) no. 5, pp. 787-796. http://geodesic.mathdoc.fr/item/MZM_1974_15_5_a15/