Contractive analytic self-mappings of the disc

Fuente: arXiv
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Main Author: Nicolau, Artur
Format: Preprint
Published: 2026
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author Nicolau, Artur
author_facet Nicolau, Artur
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2604_13825
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Contractive analytic self-mappings of the disc
Nicolau, Artur
Complex Variables
Classical Analysis and ODEs
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.
title Contractive analytic self-mappings of the disc
topic Complex Variables
Classical Analysis and ODEs
url https://arxiv.org/abs/2604.13825