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

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