Abstract:
The main result of this paper is a generalized Stieltjes criterion for the complete indeterminacy of interpolation problems in the Stieltjes class. This criterion is a generalization to limit interpolation problems of the classical Stieltjes criterion for the indeterminacy of moment problems. It is stated in terms of the Stieltjes parameters $M_j$ and $N_j$. We obtain explicit formulas for the Stieltjes parameters. General constructions are illustrated by examples of the Stieltjes moment problem and the Nevanlinna–Pick problem in the Stieltjes class.
Keywords:interpolation problem, Stieltjes moment problem, Stieltjes criterion for indeterminacy, Nevanlinna–Pick problem, Stieltjes operator function, Hankel matrix.
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