Geodesic
Criterion for the Complete Indeterminacy of the Nevanlinna--Pick Matrix Problem
Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 658-673

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We obtain a new criterion for the complete indeterminacy of the classical matrix problem and of the Nevanlinna–Pick matrix problem in terms of the convergence of two matrix series. The elements of these series are positive matrices and are expressed by analogs of the classical Schur parameters.
Keywords: Nevanlinna–Pick matrix problem, Hermitian matrix, Nevanlinna matrix function, matrix series, Schur parameter, resolvent matrix, Weyl matrix disk, Blaschke–Potapov multiplier. 
@article{MZM_2014_96_5_a2,
     author = {Yu. M. Dyukarev and A. E. Choque Rivero},
     title = {Criterion for the {Complete} {Indeterminacy} of the {Nevanlinna--Pick} {Matrix} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {658--673},
     publisher = {mathdoc},
     volume = {96},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a2/}
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Yu. M. Dyukarev; A. E. Choque Rivero. Criterion for the Complete Indeterminacy of the Nevanlinna--Pick Matrix Problem. Matematičeskie zametki, Tome 96 (2014) no. 5, pp. 658-673. http://geodesic.mathdoc.fr/item/MZM_2014_96_5_a2/