Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 3-9.

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In this paper we study some boundary properties of harmonic functions defined in the unit disk in dependence of the location of $P'$-sequences on chords and horocycles. We introduce notions of $P'$-chords, normal chords, $P'$-horocycles, and normal horocycles.
Keywords: harmonic functions, non-Euclidean circles, $P'$-sequence, $P'$-chord, horocyclic angle.
Mots-clés : radii and distances, horocyclic point
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S. L. Berberyan. Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2011), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2011_9_a0/

[1] Berberyan S. L., “O raspredelenii znachenii garmonicheskikh funktsii v edinichnom kruge”, Izv. vuzov. Matem., 2011, no. 6, 12–19

[2] 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

[3] Berberyan S. L., Gavrilov V. I., “Predelnye mnozhestva nepreryvnykh i garmonicheskikh funktsii po nekasatelnym granichnym putyam”, Math. Montisnigri, 1 (1993), 17–25 | MR

[4] Yamashita Shinji, “On Fatou- and Plessner-type theorems”, Proc. Japan. Acad., 46:6 (1970), 494–495 | DOI | MR | Zbl

[5] Berberyan S. L., “Ob uglovykh predelakh garmonicheskikh funktsii, opredelennykh v edinichnom kruge”, Vestn. Mosk. un-ta. Ser. matem., mekhan., 2007, no. 1, 55–57 | MR | Zbl

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

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

[8] Gavrilov V. I., “O nekotorykh teoremakh edinstvennosti dlya meromorfnykh funktsii”, Tr. semin. im. I. G. Petrovskogo, 1, 1975, 57–62 | MR | Zbl

[9] Bagemihl F., “Horocyclic boundary properties of meromorphic functions”, Annal. Acad. Sci. Fenn. Ser. AI, 385 (1966), 1–18 | MR

[10] Dragosh S., “Horociclic cluster sets of functions defined in the unit disc”, Nagoya Math. J., 35 (1969), 53–82 | MR | Zbl

[11] Airapetyan A. N., Gavrilov V. I., “Usileniya teoremy Meiera, kasayuscheisya granichnogo povedeniya meromorfnykh funktsii”, Izv. AN ArmSSR, 11:5 (1976), 390–399 | MR

[12] Gavrilov V. I., “O granichnom povedenii funktsii, meromorfnykh v edinichnom kruge”, Vestn. Mosk. un-ta. Ser. matem., mekhan., 1965, no. 5, 3–10 | MR | Zbl

[13] Privalov I. I., Granichnye svoistva analiticheskikh funktsii, GITTL, M.–L., 1950

[14] Kanatnikov A. N., “Ob odnoi teoreme Kollingvuda”, Vestn. Mosk. un-ta. Ser. matem., mekhan., 1976, no. 4, 1–9 | MR