Geodesic
Representation of solutions of a nomegeneous convolution equation in convex domains of the space $C^n$
Izvestiya. Mathematics , Tome 44 (1995) no. 1, pp. 69-89.

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Conditions are given under which each solution of a homogeneous convolution equation in a convex domain in $C^n$ can be represented as a series of linear combinations of integrals of elementary solutions, in terms of complete regularity of the growth of the characteristic function of the convolution operator. 
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A. S. Krivosheev. Representation of solutions of a nomegeneous convolution equation in convex domains of the space $C^n$. Izvestiya. Mathematics , Tome 44 (1995) no. 1, pp. 69-89. http://geodesic.mathdoc.fr/item/IM2_1995_44_1_a3/

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