In this paper we introduce new notions of starlikeness for a class of functions of a hypercomplex variable. We then obtain equivalent formulations for starlikeness which resemble the analogous ones in the holomorphic case such as Nevanlinna's criterion. Furthermore we give a characterization of algebraic starlikeness in terms of non- vanishing of a suitable analog of the Hadamard product.
Starlikeness for functions of a hypercomplex variable / A. Gori, F. Vlacci. - In: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9939. - 145:2(2017 Feb), pp. 791-804. [10.1090/proc/13256]
Starlikeness for functions of a hypercomplex variable
A. Gori
;
2017
Abstract
In this paper we introduce new notions of starlikeness for a class of functions of a hypercomplex variable. We then obtain equivalent formulations for starlikeness which resemble the analogous ones in the holomorphic case such as Nevanlinna's criterion. Furthermore we give a characterization of algebraic starlikeness in terms of non- vanishing of a suitable analog of the Hadamard product.
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