SEMINARIO DE ANÁLISIS COMPLEJO (COMPLEX ANALYSIS SEMINAR)

On the convolution of convex 2-gons

Adrián LLINARES
UAM
Wednesday, October 16, 2024 at 15:30 hr.

Room 520, Module 17, Department of Mathematics,
Universidad Autónoma de Madrid (Autonomous University of Madrid)
Abstract:

In 1973, Ruscheweyh and Sheil-Small showed that the convolution between two convex
mappings (that is, of two analytic functions which conformally map the unit disk
D onto a convex domain of the complex plane C) is again convex. However, further
properties of this operator are in general unknown. In this talk, we will characterize
the asymptotic growth of the (arbitrary) convolution of convex polygons of 2 edges,
thus complementing an earlier result by J. Cima.
This talk is based on a joint work with M. Chuaqui (Pontifica Universidad Cat´olica
de Chile), R. Hernández (Universidad Adolfo Ibáñez) and A. Mas (Universidad de
Valencia).