Contractive analytic self-mappings of the disc
Complex Variables
2026-04-16 v1 Classical Analysis and ODEs
Abstract
Analytic self-maps of the unit disc whose hyperbolic derivative is uniformly bounded by a constant smaller than one, are called contractive. We describe these maps in terms of their Aleksandrov-Clark measures and in terms of their inner-outer factorization. In addition, we show that contractive inner functions can be described in terms of a certain mixing property of its boundary values. We also present other results on the boundary behavior of contractive inner functions.
Cite
@article{arxiv.2604.13825,
title = {Contractive analytic self-mappings of the disc},
author = {Artur Nicolau},
journal= {arXiv preprint arXiv:2604.13825},
year = {2026}
}