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

This article is cited in 3 scientific papers (total 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.

Full text: PDF file (184 kB)
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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2011, 55:9, 1–6

Bibliographic databases:

UDC: 519.8
Received: 16.06.2010

Citation: S. L. Berberyan, “Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 9, 3–9; Russian Math. (Iz. VUZ), 55:9 (2011), 1–6

Citation in format AMSBIB
\Bibitem{Ber11}
\by S.~L.~Berberyan
\paper Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 9
\pages 3--9
\mathnet{http://mi.mathnet.ru/ivm7925}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2931770}
\elib{https://elibrary.ru/item.asp?id=16458599}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 9
\pages 1--6
\crossref{https://doi.org/10.3103/S1066369X11090015}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80055072083}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. L. Berberyan, “On boundary points of arbitrary harmonic functions”, Russian Math. (Iz. VUZ), 58:5 (2014), 1–7  mathnet  crossref
    2. S. L. Berberyan, “On boundary theorems of uniqueness for logarithmically-subharmonic functions”, Russian Math. (Iz. VUZ), 60:9 (2016), 1–6  mathnet  crossref  isi
    3. S. L. Berberian, “Refinement of the Plessner theorem and Plessner points for arbitrary harmonic functions”, Moscow University Mathematics Bulletin, 72:4 (2017), 169–172  mathnet  crossref  mathscinet  isi
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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