Abstract
Families of pairs of matrix-valued meromorphic functions\(\mathcal{P}\)(ρ,P) depending on two parameters ϱ andP are introduced. They are the projective analogues of classes of functions studied in [1] and include as special cases the projective Schur, Nevanlinna and Carathéodory classes. A two sided Nevanlinna-Pick interpolation problem is defined and solved in\(\mathcal{P}\)(ρ,P), using the fundamental matrix inequality method.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. Alpay and V. Bolotnikov. Two sided Nevanlinna-Pick interpolation for a class of matrix-valued functions.Zeitschrift für Analysis und ihre Anwendungen, 12:211–238, 1993.
D. Alpay and V. Bolotnikov. On a class of functions analytic in a half disk and an associated interpolation problem.Journal of mathematical analysis and applications, pages 1–22, 1994.
D. Alpay, P. Bruinsma, A. Dijksma, and H.S.V. de Snoo. Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II.Integral Equations Operator Theory, 14:465–500, 1991.
D. Alpay, P. Bruinsma, A. Dijksma, and H.S.V. de Snoo. Interpolation problems, extensions of symmetric operators and reproducing kernel spaces I.Operator Theory: Adv. Appl., 50, pages 35–82, 1991.
D. Alpay and H. Dym.On reproducing kernel spaces, the Schur algorithm and interpolation in a general class of domains, volume 50 ofOperator theory: advances and applications, pages 30–77. Birkhäuser Verlag, Basel, 1992.
D. Alpay and H. Dym. On a class of reproducing kernel Hilbert spaces and a new generalization of the Iohvidov's laws.Lin. Alg. Appl., 178:109–183, 1993.
D. Alpay and H. Dym. On a new class of structured reproducing kernel Hilbert spaces.J. Funct. Anal., 111:1–28, 1993.
J. Ball, I. Gohberg, and L. Rodman.Interpolation of rational matrix functions. Birkhäuser Verlag, Basel, 1990.
J. Bognar.Indefinite inner product spaces. Springer-Verlag, Berlin, 1974.
H. Dym.J-contractive matrix functions, reproducing kernel spaces and interpolation, volume 71 ofCBMS Lecture Notes. Amer. Math. Soc., Rhodes Island, 1989.
Yu. Dyukarev and V.E. Katznelson. Multiplicative and additive classes of Stieltjes analytic matrix-valued functions and interpolation problems associated with them. I.American Mathematical Society Translations, 131:55–70, 1986.
B. Fritzsche and B. Kirstein, editors.Ausgewählte Arbeiten zu den Ursprüngen der Schur-Analysis, volume 16 ofTeubner-Archiv zur Mathematik. B.G. Teubner Verlagsgesellschaft, Stuttgart-Leipzig, 1991.
I. Kovalishina. Analytic theory of a class of interpolation problems.Math. USSR Izv., 22:419–463, 1984.
I.V. Kovalishina and V.P. Potapov. An indefinite metric in the Nevanlinna-Pick problem.American Mathematical Society Translations, 138:15–20, 1988.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Alpay, D., Bolotnikov, V. Classes of pairs of meromorphic matrix valued functions generated by nonnegative kernels and associated Nevanlinna-Pick problems. Integr equ oper theory 23, 245–267 (1995). https://doi.org/10.1007/BF01198484
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01198484