2019
Том 71
№ 9

All Issues

Dyukarev Yu. M.

Articles: 4
Article (Russian)

Rational matrix functions associated with the Nevanlinna-Pick problem in the class S [a, b] and orthogonal on a compact interval

Dyukarev Yu. M., Serikova I. Yu.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2007. - 59, № 6. - pp. 764–770

We consider the interpolation Nevanlinna-Pick problem with infinitely many interpolation nodes in the class S[a, b] and rational matrix functions associated with this problem and orthogonal on the segment [a, b]. We obtain a criterion of complete indeterminacy of the Nevanlinna-Pick problem in terms of orthogonal rational matrix functions.

Article (Russian)

Degenerate Nevanlinna-Pick problem

Dyukarev Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2005. - 57, № 10. - pp. 1334–1343

A general solution of the degenerate Nevanlinna-Pick problem is described in terms of fractional-linear transformations. A resolvent matrix of the problem is obtained in the form of a J-expanding matrix of full rank.

Article (Russian)

Nevanlinna–Pick Problem for Stieltjes Matrix Functions

Dyukarev Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 3. - pp. 366-380

We consider the Nevanlinna–Pick interpolation problem for Stieltjes matrix functions. We obtain two criteria for the indeterminacy of the Nevanlinna–Pick problem with infinitely many interpolation nodes. In the indeterminate case, we describe the general solution of the Nevanlinna–Pick problem in terms of fractional-linear transformations.

Article (Russian)

An Interpolation Problem in the Class $R[a,b]$

Choque Rivero A. E., Dyukarev Yu. M.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2003. - 55, № 8. - pp. 1044-1057

We consider an interpolation problem for matrix functions of the class $R[a,b]$. In the nondegenerate case, we describe all solutions in terms of fractional linear transformations. An explicit formula for the resolvent matrix is obtained.