Geodesic
On interpolation for the Privalov classes in a disk
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1762-1775.

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The problems of interpolation on the set of simple and multiple nodes for the Privalov classes of analytic functions in the unit disk are solved in this article.
Mots-clés : interpolation, simple nodes, multiple nodes
Keywords: the Carleson condition, the Privalov classes, analytic functions, unit disk. 
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E. G. Rodikova; V. A. Bednazh. On interpolation for the Privalov classes in a disk. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1762-1775. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a144/

[1] Bednazh V. A., Description of traces, characteristic of the principal parts in the Laurent expansion of classes of meromorphic functions with restrictions on growth characteristics Nevanlinna, Thesis Abstract, St. Peter., 2007 (in Russian)

[2] Bednazh V. A., Rodikova E. G., Shamoyan F. A., “Multiple interpolation and principal parts of a Laurent series of meromorphic functions in the unit disk with power growth of the Nevanlinna characteristic”, Complex Analysis and Operator Theory, 11:1 (2017), 197–215 | DOI | MR | Zbl

[3] Carleson L., “An interpolation problem for bounded analytic functions”, Amer. J. Math., 80 (1958), 921–930 | DOI | MR | Zbl

[4] Djrbashian M. M., “Basicity of some biorthogonal systems and the solution of the multiple interpolation problem in $H^p$-classes in the halfplane”, Izv. Akad. Nauk ArmSSR, Matematika, 43:6 (1978), 1327–1384 (in Russian)

[5] Hartmann A., Massaneda X., Nicolau A., Thomas P., “Interpolation in the Nevanlinna and Smirnov classes and harmonic majorants”, J. Funct. Anal., 217:1 (2004), 1–37 | DOI | MR | Zbl

[6] Gavrilov V. I., Subbotin A. V., Efimov D. A., Boundary properties of analytic functions (further contribution), Publishing House of the Moscow University, M., 2012 (in Russian) | MR

[7] Mestrovic R., Susic J., “Interpolation in the spaces $N^p (1

+\infty)$”, Filomat, 27:2 (2013), 291–299 | DOI | MR | Zbl

[8] Naftalevic A. G., “On interpolation by functions of bounded characteristic”, Vilniaus Valst. Univ. Mokslu Darbai. Mat. Fiz. Chem. Mokslu Ser., 5 (1956), 5–27 (in Russian) | MR

[9] Nevanlinna R., Eindeutige analytische Funktionen, 2nd ed., Springer-Verlag, Berlin, 1953 | MR | Zbl

[10] Privalov I. I., Boundary properties of single-valued analytic functions, Izd. Moscow State University, M., 1941 (in Russian) | MR

[11] Rodikova E. G., “On Interpolation in the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces”, Journ. of Siberian Fed. Univ. Math. and Phys., 9:1 (2016), 69–78 | DOI | MR

[12] Rodikova E. G., “On multiple interpolation in the class of analytic functions in a disk with the Nevanlinna characeristic from Lp-spaces”, Siberian Electronic Math. Reports, 14 (2017), 264–273 (in Russian) | MR | Zbl

[13] Rodikova E. G., “Coefficient multipliers for the Privalov class in a disk”, Journ. of Siberian Fed. Univ. Math. and phys., 11:6 (2018), 723–732 | DOI | MR

[14] Seip K., Interpolating and sampling in spaces of analytic functions, University Lecture Series, 33, Amer. Math. Soc., Providence, RI, 2004 | DOI | MR

[15] Shamoyan F. A., “M. M. Dzhrbashian'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) | MR | Zbl

[16] Shamoyan F. A., Weighted spaces of analytic functions with mixed norm, Bryansk St. Univ., Bryansk, 2014

[17] Shamoyan F. A., Rodikova E. G., “On interpolation in the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic”, Journ. of Siberian Fed. Univ. Math. and Phys., 7:2 (2014), 235–243 | MR

[18] Shapiro H. S., Shields A. L., “On some interpolation problems for analytic functions”, Amer. J. Math., 83 (1961), 513–532 | DOI | MR | Zbl

[19] Vinogradov S. A., Havin V. P., “Free interpolation in $H^{\infty}$ and in some other classes of functions”, J. of Math. Sci., 47 (1974), 15–54 (in Russian) | MR | Zbl

[20] Yanagihara N., “Interpolation theorem for the class $N^+$”, Illinois J. Math., 18 (1974), 457–435 | DOI | MR | Zbl