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On interpolation in the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic. (English) Zbl 1522.30016

Summary: In this paper we solve the interpolation problem for the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic under the condition that interpolation nodes are contained in a finite union of Stolz angles.

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30E05 Moment problems and interpolation problems in the complex plane
Full Text: MNR

References:

[1] R. Nevanlinna, Eindeutige analytische Funktionen, 2nd ed., Springer-Verlag, 1953 · Zbl 0050.30302
[2] L. Carleson, “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80 (1958), 921-930 · Zbl 0085.06504 · doi:10.2307/2372840
[3] S. A. Vinogradov, V. P. Havin, “Free interpolation in \(H^\infty\) and in some other classes of functions. I”, Zap. Nauchn. Sem. LOMI, 47, 1974, 15-54 (in Russian) · Zbl 0355.41005
[4] A. G. Naftalevic, “On interpolation by functions of bounded characteristic”, Vilniaus Valst. Univ. Mokslu Darbai. Mat. Fiz. Chem. Mokslu Ser., 5 (1956), 5-27 (in Russian)
[5] A. Hartmann, X. Massaneda, A. Nicolau, P. Thomas, “Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants”, J. Funct. Anal., 217 (2004), 1-37 · Zbl 1068.30027 · doi:10.1016/j.jfa.2004.02.015
[6] J. Shapiro, A. Shields, “On some interpolation problems for analytic functions”, Amer. J. Math., 83 (1961), 513-532 · Zbl 0112.29701 · doi:10.2307/2372892
[7] K. Seip, Interpolation and sampling in spaces of analytic functions, University Lecture Series, 33, Amer. Math. Soc., Providence, 2004 · Zbl 1057.30036
[8] M. M. Djrbashian, “On the representation problem of analytic functions”, Soob. Inst. Mat. i Mekh. AN ArmSSR, 2 (1948), 3-40 (in Russian)
[9] I. I. Privalov, Boundary properties of analytic functions, Gostekhizdat, Moscow-Leningrad, 1950 (in Russian)
[10] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton University Press, 1970 · Zbl 0207.13501
[11] F. A. Shamoyan, E. N. Shubabko, “Parametrical representations of some classes of holomorphic functions in the disk”, Operator Theory: Advances and Applications, 113, Birkhauser Verlag, Basel, 2000, 331-338 · Zbl 1052.30056
[12] P. Koosis, Introduction to \(H_p\) Spaces, Cambridge University Press, 1998 · Zbl 1024.30001
[13] F. A. Shamoyan, “M. M. Dzhrbashyan”s factorization theorem and characterization of zeros of functions analytic in the disk with a majorant of bounded growth”, Izv. Akad. Nauk ArmSSR, Matematika, 13:5-6 (1978), 405-422 (in Russian) · Zbl 0411.30018
[14] F. A. Shamoyan, E. N. Shubabko, Introduction to the theory of weighted \(L^p\)-classes of meromorphic functions, Bryanskiy Gosudarstven. Universitet, Bryansk, 2009 (in Russian)
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