Abstract
We obtain new indeterminacy conditions for the matrix
Nevanlinna-Pick interpolation problem. These conditions are
formulated in terms of the convergence of two matrix series. The
elements of these series are rational matrix functions of the first
and second kind.
Отримано нові умови невизначеності для матричної
інтерполяційної задачі Неванлінни-Піка. Ці умови формулюється в
термінах збіжності двох матричних рядів. Елементами цих рядів є
раціональні матриць-функції першого і другого роду.
Key words: Nevanlinna–Pick matrix interpolation problem, Nevanlinna matrix function, resolvent matrix, Weyl matrix disk, complete indeterminacy, Blaschke–Potapov factors.
Full Text
Article Information
| Title | Indeterminacy conditions for the matrix Nevanlinna-Pick problem and rational matrix functions of the first and second kind |
| Source | Methods Funct. Anal. Topology, Vol. 28 (2022), no. 1, 25-40 |
| MathSciNet |
MR4459181 |
| Milestones | Received 18/06/2021; Revised 07/09/2021 |
| Copyright | The Author(s) 2022 (CC BY-SA) |
Authors Information
Yu. M. Dyukarev
Department of Physics, V. N. Karazin Kharkov National University, Svobody Square 4, 61202 Kharkov, Ukraine
Citation Example
Yu. M. Dyukarev, Indeterminacy conditions for the matrix Nevanlinna-Pick problem and rational matrix functions of the first and second kind, Methods Funct. Anal. Topology 28
(2022), no. 1, 25-40.
BibTex
@article {MFAT1723,
AUTHOR = {Yu. M. Dyukarev},
TITLE = {Indeterminacy conditions for the matrix Nevanlinna-Pick problem and rational matrix functions of the first and second kind},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {28},
YEAR = {2022},
NUMBER = {1},
PAGES = {25-40},
ISSN = {1029-3531},
MRNUMBER = {MR4459181},
URL = {http://mfat.imath.kiev.ua/article/?id=1723},
}
