Contractive analytic self-mappings of the disc
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918448515252224 |
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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 |