On characterization of zero sets of the weighted class of analytic functions in a disc
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 64-75 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Complete description of the zero sets of analytic functions in a unit disc, allowing growth near the given finite set of points on the boundary circle, are obtained in this paper.
@article{VMJ_2014_16_3_a6,
     author = {F. A. Shamoyan and E. G. Rodikova},
     title = {On characterization of zero sets of the weighted class of analytic functions in a~disc},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
     pages = {64--75},
     year = {2014},
     volume = {16},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a6/}
}
TY  - JOUR
AU  - F. A. Shamoyan
AU  - E. G. Rodikova
TI  - On characterization of zero sets of the weighted class of analytic functions in a disc
JO  - Vladikavkazskij matematičeskij žurnal
PY  - 2014
SP  - 64
EP  - 75
VL  - 16
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a6/
LA  - ru
ID  - VMJ_2014_16_3_a6
ER  - 
%0 Journal Article
%A F. A. Shamoyan
%A E. G. Rodikova
%T On characterization of zero sets of the weighted class of analytic functions in a disc
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 64-75
%V 16
%N 3
%U http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a6/
%G ru
%F VMJ_2014_16_3_a6
F. A. Shamoyan; E. G. Rodikova. On characterization of zero sets of the weighted class of analytic functions in a disc. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 3, pp. 64-75. http://geodesic.mathdoc.fr/item/VMJ_2014_16_3_a6/

[1] Dzhrbashyan M. M., “K probleme predstavimosti analiticheskikh funktsii”, Soobsch. Instituta matematiki i mekhaniki AN Arm. SSR, 1948, no. 2, 3–40

[2] Shapiro H. S., Shields A. L., “On the zeros of functions with finite Dirichlet integral and some related function spaces”, Math. Z., 80 (1962), 217–229 | DOI | MR | Zbl

[3] Seip K., Interpolating and sampling in spaces of analytic functions, Amer. Math. Soc., Providence, RI, 2004, 183 pp. | MR

[4] Djrbashian A. E., Shamoyan F. A., Topics in the Theory of $A^p_\alpha$ Spaces, Teubner-Texte zur Math., Leipzig, 1988, 105 pp. | MR

[5] Shamoyan F. A., “Faktorizatsionnaya teorema M. M. Dzhrbashyana i kharakterizatsiya nulei analiticheskikh funktsii s mazhorantoi konechnogo rosta”, Izv. AN Arm. SSR. Ser. Matematika, 13:5–6 (1978), 405–422 | MR | Zbl

[6] Shamoyan F. A., “O nulyakh analiticheskikh v kruge funktsii, rastuschikh vblizi ego granitsy”, Izv. AN Arm. SSR. Ser. Matematika, 18:1 (1983), 215–228 | MR

[7] Borichev A., Golinskii L., Kupin S., “A Blaschke-type condition and its application to complex Jacobi matrices”, Bulletin of the London Mathematical Society, 41 (2009), 117–123 | DOI | MR | Zbl

[8] Golinskii L., Kupin S., “A Blaschke-type condition for analytic functions on finitely connected domains. Applications to complex perturbations of a finite-band selfadjoint operator”, J. Math. Anal. Appl., 389:2 (2012), 705–712 | DOI | MR | Zbl

[9] Favorov S., Golinskii L., “Blaschke-Type Conditions for Analytic and Subharmonic Functions in the Unit Disk: Local Analogs and Inverse Problems”, Computational Methods and Func. Theory, 12 (2012), 151–166 | DOI | MR | Zbl

[10] Favorov S., Golinskii L., Blaschke-type conditions in unbounded domains, generalized convexity and applications in perturbation theory, arXiv: 1204.4283 | MR

[11] Favorov S., Radchenko L., “On Analytic and Subharmonic Functions in Unit Disc Growing Near a Part of the Boundary”, Zh. Mat. Fiz. Anal. Geom., 9:3 (2013), 304–315 | MR | Zbl

[12] Shamoyan F. A., “On some properties of zero sets of analytic functions with given majorant”, Theory functions and applications, Collections of works dedicates to the memory of M. M. Djrbashian, Luys Publishing House, Yerevan, 1995, 169–172

[13] Shamoyan F. A., “O nulyakh analiticheskikh v kruge funktsii s zadannoi mazhorantoi vblizi ego granitsy”, Matem. zametki, 85:2 (2009), 300–312 | DOI | MR | Zbl

[14] Hayman W. K., Korenblum B., “A critical growth rate for functions regular in a disk”, Michigan Math. J., 27 (1980), 21–30 | DOI | MR | Zbl

[15] Bykov S. V., Faktorizatsionnye predstavleniya i svoistva kornevykh mnozhestv vesovykh klassov analiticheskikh funktsii, Diss. $\dots$ kand. fiz.-mat. nauk, BGU, Bryansk, 2010, 130 pp.

[16] Titchmarsh E., Teoriya funktsii, Nauka, M., 1980, 480 pp. | MR