Directional Convexity of Convolutions of Harmonic Functions

Jay M. Jahangiri and Raj Kumar Garg

International Journal of Mathematics and Mathematical Sciences, 2019, vol. 2019, 1-6

Abstract:

Harmonic functions can be constructed using two analytic functions acting as their analytic and coanalytic parts but the prediction of the behavior of convolution of harmonic functions, unlike the convolution of analytic functions, proved to be challenging. In this paper we use the shear construction of harmonic mappings and introduce dilatation conditions that guarantee the convolution of two harmonic functions to be harmonic and convex in the direction of imaginary axis.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:5731830

DOI: 10.1155/2019/5731830

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