Geodesic
Step-by-step solving of ordered interpolational problem for Stieltjes functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 18-32

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we investigate a step-by-step solving of ordered generalized interpolation problems for the Stieltjes matrix functions and obtain a multiplicative representation of the sequence of resolvent matrices. The matrix factors in multiplicative representation of resolvent matrices are expressed through the Schur–Stieltjes parameters, for which we obtain explicit formulas, and adduce an algorithm of step-by-step solving of Stieltjes type interpolation problems. As examples, we consider step-by-step solving of Stieltjes matrix moment problem, Nevanlinna–Pick problem and Caratheodory problem.
Keywords: interpolational problems, Stieltjes functions, criterion of indeterminancy, orthonormed matrix-functions. 
@article{IVM_2017_6_a2,
     author = {Yu. M. Dyukarev and I. Yu. Serikova},
     title = {Step-by-step solving of ordered interpolational problem for {Stieltjes} functions},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {18--32},
     publisher = {mathdoc},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2017_6_a2/}
}
TY  - JOUR
AU  - Yu. M. Dyukarev
AU  - I. Yu. Serikova
TI  - Step-by-step solving of ordered interpolational problem for Stieltjes functions
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2017
SP  - 18
EP  - 32
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2017_6_a2/
LA  - ru
ID  - IVM_2017_6_a2
ER  - 
%0 Journal Article
%A Yu. M. Dyukarev
%A I. Yu. Serikova
%T Step-by-step solving of ordered interpolational problem for Stieltjes functions
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2017
%P 18-32
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2017_6_a2/
%G ru
%F IVM_2017_6_a2
Yu. M. Dyukarev; I. Yu. Serikova. Step-by-step solving of ordered interpolational problem for Stieltjes functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2017), pp. 18-32. http://geodesic.mathdoc.fr/item/IVM_2017_6_a2/