Inner Functions, Möbius Distortion and Angular Derivatives
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915375569960960 |
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| author | Bampouras, Konstantinos Nicolau, Artur |
| author_facet | Bampouras, Konstantinos Nicolau, Artur |
| contents | We prove that an inner function has finite $\mathcal{L} (p)$-entropy if and only if its accumulated Möbius distortion is in $L^p$, $0<p<\infty$. We also study the support of the positive singular measures such that their corresponding singular inner functions have finite $\mathcal{L} (p)$-entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03414 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Inner Functions, Möbius Distortion and Angular Derivatives Bampouras, Konstantinos Nicolau, Artur Complex Variables Classical Analysis and ODEs 30J05, 30J15, 30H15, 30C80 We prove that an inner function has finite $\mathcal{L} (p)$-entropy if and only if its accumulated Möbius distortion is in $L^p$, $0<p<\infty$. We also study the support of the positive singular measures such that their corresponding singular inner functions have finite $\mathcal{L} (p)$-entropy. |
| title | Inner Functions, Möbius Distortion and Angular Derivatives |
| topic | Complex Variables Classical Analysis and ODEs 30J05, 30J15, 30H15, 30C80 |
| url | https://arxiv.org/abs/2503.03414 |