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In the space of all entire functions it is solved the problem ofinterpolation taking into account multiplicities by sums of the series ofexponentials with the exponents from a given set. It is found a criterion ofsolubility of the problem in the case when all infinite portions ofinterpolation nodes are situated on a finite system of rays. It is alsodisclosed that the problem is equivalent to particular problems of simpleinterpolation, as well as of point-wise crude approximation, by sums of theseries of exponentials.

Interpolation by sums of the series of exponentials in $H (\mathbb C)$ with interpolation nodes on the rays