This article is cited in 8 papers

The problem concerning the epimorphicity of a convolution operator in convex domains

O. V. Epifanov

Rostov State University

Abstract: We deduce an epimorphicity criterion for the convolution operator
$$ (a*x)(z)=\frac1{2\pi i}\oint x(t)\tilde a(t-z)\,dt, $$
acting from a space of functions analytic in a convex domain into another such space; $\tilde a(z)$ is the Borel transformation of the exponential function $a(z)$.

UDC: 517.43

Received: 15.11.1973

 English version: Mathematical Notes, 1974, 16:3, 837–841

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