Geodesic
Synthesis in the kernel of the three-way convolution operator
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 130-141.

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One says that an approximation theorem holds for a homogeneous convolution-type equation if any solution of this equation is approximated by its elementary solutions. In this paper, we state a necessary and sufficient condition for the validity of the approximation theorem for the homogeneous equation of three-way convolution for any choice of a convex domain and its characteristic function.
Keywords: exponential synthesis, kernel of operator, convolution-type operator, invariant subspace, analytic function. 
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A. A. Tatarkin; A. B. Shishkin. Synthesis in the kernel of the three-way convolution operator. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 4, Tome 193 (2021), pp. 130-141. http://geodesic.mathdoc.fr/item/INTO_2021_193_a13/

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