On Analytic and Subharmonic Functions in Unit Disc Growing Near a Part of the Boundary
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 304-315
S. Ju. Favorov; L. D. Radchenko. On Analytic and Subharmonic Functions in Unit Disc Growing Near a Part of the Boundary. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013) no. 3, pp. 304-315. http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a1/
@article{JMAG_2013_9_3_a1,
     author = {S. Ju. Favorov and L. D. Radchenko},
     title = {On {Analytic} and {Subharmonic} {Functions} in {Unit} {Disc} {Growing} {Near} a {Part} of the {Boundary}},
     journal = {\v{Z}urnal matemati\v{c}eskoj fiziki, analiza, geometrii},
     pages = {304--315},
     year = {2013},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a1/}
}
TY  - JOUR
AU  - S. Ju. Favorov
AU  - L. D. Radchenko
TI  - On Analytic and Subharmonic Functions in Unit Disc Growing Near a Part of the Boundary
JO  - Žurnal matematičeskoj fiziki, analiza, geometrii
PY  - 2013
SP  - 304
EP  - 315
VL  - 9
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a1/
LA  - en
ID  - JMAG_2013_9_3_a1
ER  - 
%0 Journal Article
%A S. Ju. Favorov
%A L. D. Radchenko
%T On Analytic and Subharmonic Functions in Unit Disc Growing Near a Part of the Boundary
%J Žurnal matematičeskoj fiziki, analiza, geometrii
%D 2013
%P 304-315
%V 9
%N 3
%U http://geodesic.mathdoc.fr/item/JMAG_2013_9_3_a1/
%G en
%F JMAG_2013_9_3_a1

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

In the paper there was found an analog of the Blaschke condition for analytic and subharmonic functions in the unit disc, which grow at most as a given function $\varphi$ near some subset of the boundary.

[1] S. Favorov, L. Golinskii, “A Blaschke-type Condition for Analytic and Subharmonic Functions and Application to Contraction Operators”, Amer. Math. Soc. Transl., 226:2 (2009), 37–47 | MR | Zbl

[2] G. Kramer, Mathematical Methods of Statistic, Mir, M., 1975 (in Russian) | MR

[3] T. Ransford, Potential Theory in the Complex Plane, London Math. Soc. Student Texts, 28, Cambridge Univ. Press, Cambridge, 1995 | MR | Zbl

[4] J. Garnett, Bounded Analytic Functions, Graduate Texts in Mathematics, 236, Springer, New York, 2007 | MR

[5] A. Borichev, L. Golinskii, S. Kupin, “A Blaschke-type Condition and its Application to Complex Jacobi Matrices”, Bull. London Math. Soc., 41 (2009), 117–123 | DOI | MR | Zbl

[6] M. M. Djrbashian, “Theory of Factorization of Functions Meromorphic in the Disk”, Proc. of the ICM (Vancouver, B.C., 1974), v. 2, USA, 1975, 197–202

[7] W. K. Hayman, B. Korenblum, “A Critical Growth Rate for Functions Regular in a Disk”, Michigan Math. J., 27 (1980), 21–30 | DOI | MR | Zbl

[8] F. A. Shamoyan, “On Zeros of Analytic in the Disc Functions Growing near its Boundary”, J. Contemp. Math. Anal., Armen. Acad. Sci., 18:1 (1983) | MR | Zbl

[9] A. M. Jerbashian, “On the Theory of Weighted Classes of Area Integrable Regular Functions”, Complex Variables, 50 (2005), 155–183 | DOI | MR | Zbl

[10] R. Nevanlinna, Single-Valued Analytic Functions, Gostehizdat, M., 1941 (in Russian)