Geodesic
On interpolation in the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 69-78.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we solve the interpolation problem for the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces under the condition that interpolation nodes are contained in a finite union of Stolz angles.
Keywords: holomorphic functions, the Nevanlinna characteristic, Stolz angles.
Mots-clés : interpolation 
@article{JSFU_2016_9_1_a7,
     author = {Eugenia G. Rodikova},
     title = {On interpolation in the class of analytic functions in the unit disk with the {Nevanlinna} characteristic from {Lp-spaces}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {69--78},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a7/}
}
TY  - JOUR
AU  - Eugenia G. Rodikova
TI  - On interpolation in the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2016
SP  - 69
EP  - 78
VL  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a7/
LA  - en
ID  - JSFU_2016_9_1_a7
ER  - 
%0 Journal Article
%A Eugenia G. Rodikova
%T On interpolation in the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2016
%P 69-78
%V 9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a7/
%G en
%F JSFU_2016_9_1_a7
Eugenia G. Rodikova. On interpolation in the class of analytic functions in the unit disk with the Nevanlinna characteristic from Lp-spaces. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 69-78. http://geodesic.mathdoc.fr/item/JSFU_2016_9_1_a7/

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

[3] M. M. Djrbashian, “On the representation problem of analytic functions”, Soob. Inst. Math. i Mekh. AN ArmSSR, 2 (1948), 3–40 (in Russian)

[4] M. M. Djrbashian, “Basicity of some biorthogonal systems and the solution of the multiple interpolation problem in the classes Hp in the halfplane”, Izv. Acad. Nauk SSSR. Ser. Matem., 42:6 (1978), 1322–1384 (in Russian) | MR

[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 | DOI | MR | Zbl

[6] A. M. Kotochigov, Free interpolation in Jordan domains, Thesis Abstract, The Russian Academy of Sciences, St. Petersburg Department of Steklov Institute of Mathematics, St. Peter., 2001 (in Russian)

[7] 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) | MR

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

[9] E. G. Rodikova, “On estimates of the expansion coefficients of certain classes of analytic functions in the disk”, Abstracts of Petrozavodsk international conference “Complex analysis and its applications”, Petrozavodsk St. Univ., 2012, 64–69 (in Russian)

[10] F. A. Shamoyan, E. G. Rodikova, “On interpolation in the class of analytic functions in the unit disk with power growth of the Nevanlinna characteristic”, Journal of Sberian Federal University. Mathematics $\$ Physics, 7:2 (2014), 235–243

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

[12] K. Seip, Interpolation and sampling in spaces of analytic functions, University Lecture Series, 33, Amer. Math. Soc., Providence, 2004 | MR | Zbl

[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) | MR | Zbl

[14] F. A. Shamoyan, “Parametric representation and description of the root sets of weighted classes of holomorphic functions in a disk”, Sib. Mat. Zhurn., 40:6 (1999), 1422–1440 (in Russian) | MR | Zbl

[15] F. A. Shamoyan, Weighted spaces of analytic functions with mixed norm, Bryansk Gos. Univ., Bryansk, 2014 (in Russian)

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