Interpolation with multiplicity by series of exponentials in $H(\mathbb C)$ with nodes on the real axis

Abstract

In the space of entire functions we study an interpolation problem with multiplicity by the functions from a closed subspace which is invariant in respect to the operator of differentiation. The discrete set of the nodes for the interpolation with multiplicity is located on the real axis in the complex plane. The proof is based on the passage from the subspace to its subspace consisting of all series of exponentials converging in the topology of uniform convergence on compact sets. We obtain a criterion for the solvability of the interpolation problem with real nodes having multiplicity by series of exponentials in the terms of location of exponents of exponentials.