Criterion for complete indeterminacy of limiting interpolation problem of Stieltjes type in terms of orthonormal matrix-functions

The main goal of the paper is to study the ordered sequences of generalized interpolation problems and the limiting interpolation problem in the Stieltjes class by means of 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.