The criterion for the complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of the orthonormal matrix functions

The main goal of this paper is to study the ordered sequences of generalized interpolation problems and the limiting interpolation problem in the Stieltjes class by using the orthonormal matrix functions. We obtain explicit formulas for the orthonormal matrix functions. The main result of the paper is a criterion for the complete indeterminacy of limiting interpolation problem in the Stieltjes class. General constructions are illustrated by examples of the Stieltjes moment problem and the Nevanlinna–Pick problem in the Stieltjes class.