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

In the space of holomorphic functions in a convex domain, we study a problem on interpolation by sums of the series of exponentials converging uniformly on compact subsets of the domain. The discrete set of multiple interpolation nodes is located on the real axis in the domain and has the unique finite accumulation point. We obtain a solvability criterion in terms of distribution of limit directions at infinity for the exponents of exponentials.