A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems

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.