ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 30 Anna Łazińska, Zbigniew J. Jakubowski, University of Łódź, Poland On a class of mappings harmonic in the half-plane, with a normalization at infinity In the communication, a family of typically-real functions harmonic in the right half-plane will be presented. We consider the class of functions F = h + \overline{g} harmonic in Π^{+} = \{z ∈ C : ℜz > 0\}, such that:

1) ℑF (z) = 0 ⟺ ℑz = 0, z ∈ Π^{+}; 2) lim_{Π^{+}∋z→∞}(F (z) − z) = a_{F};

3) lim_{Π^{+}∋z→∞} ℜg(z) = α_{g}, a_{F} , α_{g} ∈ R ([2]).

The results are based, among others, on [1]. References: [1] Z. J. Jakubowski, A. Łazińska, On typically-real functions …, Folia Sci. Univ. Techn. Resoviensis 129 (16) (1994), 5-24.

[2] Z. J. Jakubowski, A. Łazińska, On a class of mappings harmonic …, Trudy Petrozavodskovo Gosudarstvennovo Univ. 4 (1997), 139-155.