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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2011 Number 9, Pages 3–9 (Mi ivm7925)

This article is cited in 3 papers

Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions

S. L. Berberyan

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

Abstract: 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, radii and distances, $P'$-sequence, $P'$-chord, horocyclic point, horocyclic angle.

UDC: 519.8

Received: 16.06.2010


 English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:9, 1–6

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