Solvability criterion for multiple interpolation problem in preimage of convolution operator

Abstract

In this paper we find a solvability criterion for the multiple interpolation problem in the preimage of a convolution operator and, consequently, a criterion for the solvability of Abel — Goncharov problem in the same space. When the kernel of the operator serves as the preimage, uniqueness of the solution to these problems holds provided the set of interpolation nodes is the uniqueness set in the kernel of the convolution operator.