UNIVALENCE OF HARMONIC FUNCTIONS, PROBLEM OF PONNUSAMY AND SAIRAM, AND CONSTRUCTIONS OF UNIVALENT POLYNOMIALS

Abstract

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 0 H = S 0 H(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