Starlikeness for functions of a hypercomplex variable
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- by Anna Gori and Fabio Vlacci PDF
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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.References
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Additional Information
- Anna Gori
- Affiliation: Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy
- Email: anna.gori@unimi.it
- Fabio Vlacci
- Affiliation: Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze Viale Morgagni 67/A, 50134 Firenze, Italy
- MR Author ID: 349650
- Email: vlacci@math.unifi.it
- Received by editor(s): July 27, 2015
- Received by editor(s) in revised form: March 3, 2016, April 7, 2016, and April 20, 2016
- Published electronically: August 23, 2016
- Additional Notes: This work was partially supported by Progetto MIUR di Rilevante Interesse Nazionale PRIN 2010-11 Varietà reali e complesse: geometria, topologia e analisi armonica. The research that led to the present paper was partially supported by a grant of the group GNSAGA of Istituto Nazionale di Alta Matematica “F: Severi”.
- Communicated by: Franc Forstneric
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 791-804
- MSC (2010): Primary 30G35, 30C45
- DOI: https://doi.org/10.1090/proc/13256
- MathSciNet review: 3577878