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.
Citation:
S. L. Berberyan, “The distribution of values of harmonic functions in the unit disk”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 6, 12–19; Russian Math. (Iz. VUZ), 55:6 (2011), 9–14
\Bibitem{Ber11}
\by S.~L.~Berberyan
\paper The distribution of values of harmonic functions in the unit disk
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2011
\issue 6
\pages 12--19
\mathnet{http://mi.mathnet.ru/ivm7499}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2931700}
\elib{https://elibrary.ru/item.asp?id=15705508}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2011
\vol 55
\issue 6
\pages 9--14
\crossref{https://doi.org/10.3103/S1066369X11060028}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80051646912}
Linking options:
https://www.mathnet.ru/eng/ivm7499
https://www.mathnet.ru/eng/ivm/y2011/i6/p12
This publication is cited in the following 5 articles:
S. L. Berberyan, “Meyer points and refined Meyer points for arbitrary harmonic functions”, Russian Math. (Iz. VUZ), 66:5 (2022), 21–25
S. L. Berberian, “Refinement of the Plessner theorem and Plessner points for arbitrary harmonic functions”, Moscow University Mathematics Bulletin, 72:4 (2017), 169–172
S. L. Berberyan, “On boundary theorems of uniqueness for logarithmically-subharmonic functions”, Russian Math. (Iz. VUZ), 60:9 (2016), 1–6
S. L. Berberyan, “On boundary points of arbitrary harmonic functions”, Russian Math. (Iz. VUZ), 58:5 (2014), 1–7
S. L. Berberyan, “Some applications of $P'$-sequences in studying boundary properties of arbitrary harmonic functions”, Russian Math. (Iz. VUZ), 55:9 (2011), 1–6
Citation in format AMSBIB
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