Slice entire functions of quaternionic variable of bounded index
UDC 517.55+512.78 We continue our investigations of the local properties of entire slice regular functions of quaternionic variable. For this class of functions, we introduce the notion of index. The boundedness of index is characterized by the local behavior of the maximum modulus of slice de...
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| Date: | 2026 |
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| Main Authors: | , , , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8927 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.55+512.78
We continue our investigations of the local properties of entire slice regular functions of quaternionic variable. For this class of functions, we introduce the notion of index. The boundedness of index is characterized by the local behavior of the maximum modulus of slice derivative on certain discs. The corresponding maximum is uniformly estimated by the value of the modulus of slice derivative at the center of the disc. The presented results are quaternionic generalizations of the known Fricke theorems for entire functions of complex variable. |
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| DOI: | 10.3842/umzh.v77i5.8927 |