This article is cited in 7 papers

Solvability of a convolution equation in convex domains

O. V. Epifanov

Rostov State University

Abstract: 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.

UDC: 517.43

Received: 01.06.1973

 English version: Mathematical Notes, 1974, 15:5, 472–477

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