Sufficient conditions in the two-functional conjecture for univalent functions
Complex Variables
2012-10-16 v1
Abstract
The two-functional conjecture says that if a function f analytic and univalent in the unit disk maximizes Re{L} and Re{M} for two continuous linear functionals L and M, L is not equal to cM for any c>0, then f is a rotation of the Koebe function. We use the Loewner differential equation to obtain sufficient conditions in the two-functional conjecture and compare the sufficient conditions with necessary conditions.
Cite
@article{arxiv.1210.3996,
title = {Sufficient conditions in the two-functional conjecture for univalent functions},
author = {Dmitri Prokhorov},
journal= {arXiv preprint arXiv:1210.3996},
year = {2012}
}
Comments
10 pages