RUS  ENG
Full version
JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2011 Number 6, Pages 12–19 (Mi ivm7499)

This article is cited in 5 papers

The distribution of values of harmonic functions in the unit disk

S. L. Berberyan

Chair of Mathematics and Mathematical Modeling, Russian-Armenian (Slavonic) University, Yerevan, Republic of Armenia

Abstract: 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.

UDC: 517.538

Received: 16.02.2010
Revised: 13.03.2010


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:6, 9–14

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2024