Geodesic
The distribution of values of harmonic functions in the unit disk
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 12-19

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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. 
@article{IVM_2011_6_a1,
     author = {S. L. Berberyan},
     title = {The distribution of values of harmonic functions in the unit disk},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {12--19},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/}
}
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S. L. Berberyan. The distribution of values of harmonic functions in the unit disk. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 12-19. http://geodesic.mathdoc.fr/item/IVM_2011_6_a1/