Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
I. V. Kovalishina and V. P. Potapov, “Indefinite metric in the Nevanlinna-Pick problem,” Dokl. Akad. Nauk Arm. SSR, 59, Issue 1, 17–22 (1974).
V. P. Potapov, “The multiplicative structure of J-contractive matrix functions,” Tr. Mosk. Mat. Obshch., 4, 125–236 (1955).
I. V. Kovalishina and V. P. Potapov, Integral Representation of Hermite Positive Functions [in Russian], Dep. in VINITI, No. 298-81, Kharkov (1981).
I. V. Kovalishina, “Analytic theory of one class of interpolation problems,” Izv. Akad. Nauk SSR, Ser. Mat., 47, No. 3, 455–497 (1983).
V. K. Dubovoi, “Indefinite metric in the Schur interpolation problem for analytic functions,” Teor. Funkts. Funkts. Anal. Prilozhen., 42, 46–57 (1984).
V. Bolotnikov, “On degenerate Hamburger moment problem and extensions of nonnegative Hankel block matrices,” Integr. Equat. Oper. Theory, 25, No. 3, 253–276 (1996).
V. Bolotnikov and H. Dym, “On degenerate interpolation, entropy and extremal problems for Schur functions,” Integr. Equat. Oper. Theory, 28, No. 2, 275–292 (1998).
Yu. V. Dyukarev, “Maximum principle for Stieltjes pairs of analytic matrix functions,” Visn. Khark. Nats. Univ., Mat., Prikl. Mat. Mekh., No. 542, 35–41 (2002).
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 57, No. 10, pp. 1334–1343, October, 2005.
Rights and permissions
About this article
Cite this article
Dyukarev, Y.M. Degenerate Nevanlinna-Pick problem. Ukr Math J 57, 1559–1570 (2005). https://doi.org/10.1007/s11253-006-0014-8
Received:
Issue Date:
DOI: https://doi.org/10.1007/s11253-006-0014-8