Ufa Mathematical Journal
    Volume 5, Number 3, pp. 127-140

    Interpolation with multiplicity by series of exponentials in $H(\mathds{C})$ with nodes on the real axis.

    Merzlyakov S. G., Popenov S.V.


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    In the space of entire functions, we study the problem on interpolation with multiplicity by the functions from a closed subspace which is invariant with 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 solvability criterion for the problem of interpolation with multiplicity by series of exponentials for real nodes in the terms of location of exponents of exponentials.