Convolution equations in the complex domain

This article investigates analytic solutions of a convolution equation and of systems of two convolution equations with a single unknown function. The characteristic functions of all the convolution operators studied here are entire functions of exponential type. A general representation is determined for solutions of homogeneous and inhomogeneous equations and of systems of such equations in the form of absolutely convergent series in entire functions (as a rule, exponentials forming an absolutely representing system). A criterion is established for solvability of a system of two inhomogeneous convolution equations with a single unknown function. The main results are obtained with the help of nontrivial expansions of zero in convex domains with respect to functions forming an absolutely representing system.
Bibliography: 19 titles.