Abstract
Versions of the Nevanlinna-Pick interpolation problem with boundary interpolation nodes and boundary interpolated values are investigated.
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References
V. M. Adamyan, D. Z. Arov and M. G. Kreîn,Infinite Hankel matrices and generalized problems of Carathéodory-Fejér and I. Schur, Funktsional Anal. i Prilozhen.2 (1968), No. 4, 1–17.
J. A. Ball,Interpolation problems of Pick-Nevanlinna and Loewner type for meromorphic matrix functions, Integral Equations and Operator Theory6 (1983) 804–840.
J. A. Ball and J. W. Helton,Interpolation problems of Pick-Nevanlinna and Loewner types for meromorphic matrix functions: parameterization of the set of all solutions, Integral Equations and Operator Theory9 (1986), 155–203.
C. Carathéodory,Über die Winkelderivierten von beschränkten Funktionen, Sitzungber. Preuss. Acad. Wiss. (1929), 39–52.
D. N. Clark,One dimensional perturbations of restricted shifts, J. Analyse Math.25 (1972), 169–191.
Ph. Delsarte, Y. Genin and Y. Kamp,The Nevanlinna-Pick problem for matrix-valued functions, SIAM J. Appl. Math.36 (1979), 47–61.
S. Kheifets,Abstract interpolation problem and applications, Holomorphic Spaces, S. Axler, J. McCarthy and D. Sarason (Editors), Cambridge University Press, to appear.
D. M. Kotelyanskiî,On certain applications of quadratic forms to the Nevanlinna-Pick problem, Zh. Inst. Mat. Akad. Nauk. URSR 1937, No. 1, 73–88.
I. V. Kovalishina,On the “boundary derivative” of contractive analytic matrix functions in the disk, Kharkov Engineering Institute of Railway Transportation, Kharkov, 1982. Deposited Viniti 1983, N 2709.
M. G. Kreîn,General theorems about positive definite functionals, Some Questions in the Theory of Moments, N. I. Achieser and M. G. Krein, Translations of Mathematical Monographs, Vol. 2, American Mathematical Society, Providence, 1962, pp. 124–153.
R. Nevanlinna,Über beschränkte Funktionen die in gegebene Punkten vorgeschreibene Werte annehmen. Ann. Acad. Sci. Fenn. Ser. A13 (1919), No. 1.
R. Nevanlinna,Über beschränkte analytische Funktionen., Ann. Acad. Sci. Fenn. Ser. A32 (1929), No. 7.
R. Nevanlinna,Remarques sur le lemme de Schwarz, Comptes Rendus Acad. Sci. Paris188 (1929), 1027–1029.
G. Pick,Über die Beschränkungen analytischen Funktionen, welche durch vorgegebene Functionswerte bewirkt werden, Math. Ann.77 (1916), 7–23.
M. Riesz,Sur certaines inégalités dans la théorie des fonctions, Fysiogr. Sällsk. Lund Forh.1 (1931), Nr.4, 18–38.
D. Sarason,Sub-Hardy Hilbert spaces in the unit disk, University of Arkansas Lecture Series in the Mathematical Sciences, No. 10, Wiley, New York, 1994.
B. Sz.-Nagy and A. Korányi,Relations d'un problème de Nevanlinna et Pick avec la théorie des operatéurs de l'espace hilbertien, Acta Math. Acad. Sci. Hungar.7 (1957), 295–303.