Geodesic
Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials
Problemy analiza, Tome 3 (2014) no. 2, pp. 59-73

Voir la notice de l'article provenant de la source Math-Net.Ru

The criteria of the univalence of a harmonic mapping is obtained in this paper. Particularly, it permits to formulate the hypothesis of the harmonic function classes equality $S_H^0=S_H^0(S)$ (hypothesis of Ponnusamy and Sairam), in analytic form. The method of construction of the univalent harmonic polynomials with desired properties, according to a given harmonic function, is obtained by means of the univalence criteria.
Keywords: harmonic functions, criteria of the univalence, harmonic univalent polynomials. 
@article{PA_2014_3_2_a4,
     author = {V. V. Starkov},
     title = {Univalence of harmonic functions, problem of {Ponnusamy} and {Sairam,} and constructions of univalent polynomials},
     journal = {Problemy analiza},
     pages = {59--73},
     publisher = {mathdoc},
     volume = {3},
     number = {2},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2014_3_2_a4/}
}
TY  - JOUR
AU  - V. V. Starkov
TI  - Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials
JO  - Problemy analiza
PY  - 2014
SP  - 59
EP  - 73
VL  - 3
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PA_2014_3_2_a4/
LA  - en
ID  - PA_2014_3_2_a4
ER  - 
%0 Journal Article
%A V. V. Starkov
%T Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials
%J Problemy analiza
%D 2014
%P 59-73
%V 3
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PA_2014_3_2_a4/
%G en
%F PA_2014_3_2_a4
V. V. Starkov. Univalence of harmonic functions, problem of Ponnusamy and Sairam, and constructions of univalent polynomials. Problemy analiza, Tome 3 (2014) no. 2, pp. 59-73. http://geodesic.mathdoc.fr/item/PA_2014_3_2_a4/