NONTRIVIAL EXPANSIONS OF ZERO IN ABSOLUTELY REPRESENTING SYSTEMS. APPLICATIONS TO CONVOLUTION OPERATORS

Abstract

By using a general representation of nontrivial expansions of zero in absolutely representing systems of the form , where , is the Mittag-Leffler function, and are complex numbers, the author obtains a number of results in the theory of -convolution operators in spaces of functions that are analytic in -convex domains (a description of the general solution of a homogeneous -convolution equation and of systems of such equations, a topological description of the kernel of a -convolution operator, the construction of principal solutions, and a criterion for factorization).