Convolution equations in the complex domain

Yu. F. Korobeinik

Sbornik. Mathematics, Tome 55 (1986) no. 1, pp. 171-194

Résumé

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.

Bibliographie

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