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arXiv · 2604.13825

Contractive analytic self-mappings of the disc

Artur Nicolau
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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.

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Artur Nicolau. 2026-04-15. Contractive analytic self-mappings of the disc. https://arxiv.org/abs/2604.13825

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