Geodesic
A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems
Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 23-39

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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.
Mots-clés : interpolation problem, Stieltjes moment problem
Keywords: Stieltjes criterion for indeterminacy, Nevanlinna–Pick problem, Stieltjes operator function, Hankel matrix. 
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     author = {Yu. M. Dyukarev},
     title = {A {Generalized} {Stieltjes} {Criterion} for the {Complete} {Indeterminacy} of {Interpolation} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
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     number = {1},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a1/}
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Yu. M. Dyukarev. A Generalized Stieltjes Criterion for the Complete Indeterminacy of Interpolation Problems. Matematičeskie zametki, Tome 84 (2008) no. 1, pp. 23-39. http://geodesic.mathdoc.fr/item/MZM_2008_84_1_a1/