Geodesic
The distribution of values of harmonic functions in the unit disk
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 12-19.

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

In this paper we study the distribution of values of harmonic functions in non-Euclidean circles. We introduce the notion of a $P'$-sequence, which enables us to characterize the class of normal harmonic functions defined in the unit circle. We obtain sufficient conditions for the existence of such sequences and give examples which show that these conditions are essential in the stated theorems.
Keywords: harmonic functions, angular limit, normal harmonic functions, non-Euclidean circles, $P$-sequence, $P'$-sequence. 
@article{IVM_2011_6_a1,
     author = {S. L. Berberyan},
     title = {The distribution of values of harmonic functions in the unit disk},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--19},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/}
}
TY  - JOUR
AU  - S. L. Berberyan
TI  - The distribution of values of harmonic functions in the unit disk
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 12
EP  - 19
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/
LA  - ru
ID  - IVM_2011_6_a1
ER  - 
%0 Journal Article
%A S. L. Berberyan
%T The distribution of values of harmonic functions in the unit disk
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 12-19
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/
%G ru
%F IVM_2011_6_a1
S. L. Berberyan. The distribution of values of harmonic functions in the unit disk. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 12-19. http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/

[1] Gavrilov V. I., “Normalnye funktsii i pochti periodicheskie funktsii”, DAN SSSR, 240:4 (1978), 768–770 | MR | Zbl

[2] Gavrilov V. I., “O raspredelenii znachenii meromorfnykh v edinichnom kruge funktsii, ne yavlyayuschikhsya normalnymi”, Matem. sb., 67(109):3 (1965), 408–427 | MR | Zbl

[3] Lappan P., “Some results on harmonic normal functions”, Math. Zeitschr., 90:1 (1965), 155–159 | DOI | MR | Zbl

[4] Lappan P., “Fatous points of harmonic normal functions and uniformly normal functions”, Math. Zeitschr., 102:3 (1967), 110–114 | DOI | MR | Zbl

[5] Bagemihl F., Seidel W., “Sequential and continuous limits of meromorphic functions”, Annal. Acad. Scien. Fenn. Ser. A, 280 (1960), 1–17 | MR

[6] Gavrilov V. I., Zakharyan V. S., Subbotin A. V., “Lineino-topologicheskie svoistva maksimalnykh prostranstv Khardi garmonicheskikh funktsii v kruge”, Dokl. NAN Armenii, 102:3 (2002), 203–209 | MR

[7] Berberyan S. L., “Ob uglovykh granichnykh znacheniyakh normalnykh nepreryvnykh funktsii”, Izv. vuzov. Matematika, 1986, no. 3, 22–28 | MR | Zbl

[8] Berberyan S. L., “Ob uglovykh predelakh garmonicheskikh funktsii, opredelennykh v edinichnom kruge”, Vestnik MGU. Ser. Matem., mekhan., 2007, no. 1, 55–57 | MR | Zbl

[9] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950, 336 pp. | MR

[10] Nosiro K., Predelnye mnozhestva, In. lit., M., 1963, 253 pp.

[11] Lovater A., “Granichnoe povedenie analiticheskikh funktsii”, Itogi nauki i tekhniki. Matematicheskii analiz, 10, 1973, 99–259 | MR | Zbl

[12] Solomentsev E. D., “Garmonicheskie i subgarmonicheskie funktsii i ikh obobscheniya”, Itogi nauki. Ser. Mat. anal. Teor. veroyatn. Regulir. 1962, VINITI, M., 1964, 83–100 | MR | Zbl

[13] Lehto O., Virtanen K. I., “Boundary behaviour and normal meromorphic functions”, Acta Math., 97:1–2 (1957), 47–65 | DOI | MR | Zbl