Interpolation by means of series of exponentials in H(D) with real nodes

TL;DR

This paper investigates the interpolation problem in holomorphic function spaces using sums of exponential series with real nodes, providing a criterion based on the distribution of limit directions of exponents.

Contribution

It introduces a new criterion for the solvability of exponential series interpolation with real nodes in convex domains, considering the distribution of limit directions.

Findings

Interpolation series converge uniformly on compact sets

Criterion relates solvability to distribution of limit directions

Nodes are on the real axis with a finite limit point

Abstract

In the space of holomorphic functions in a convex domain it is studied the interpolation problem by means of sums of the series of exponentials converging uniformly on all compact sets of the domain. The discrete set of the interpolation nodes with multiplicities is located on the real axis in the domain and it has the only finite limit point. It is obtained a criterion for solvability of the problem in the terms of distribution of limit directions of exponents of exponentials at infinity.