On a functional equation related to an automorphism of a unit circle
In this article the complete description of the decisions of a functional equation (1 + ¯ζeiθ z)pf (z) = f (ω(0))f (z) is given, where ω(z) = (eiθ z + ζ )/(1 + ¯ζeiθ z) – automorphism of a unit circle E and the decisions are searched among analytical in E functions. It is established, that research...
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2023-09-01
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| Series: | Lietuvos Matematikos Rinkinys |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/LMR/article/view/30568 |
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| Summary: | In this article the complete description of the decisions of a functional equation
(1 + ¯ζeiθ z)pf (z) = f (ω(0))f (z)
is given, where ω(z) = (eiθ z + ζ )/(1 + ¯ζeiθ z) – automorphism of a unit circle E and the decisions are searched among analytical in E functions. It is established, that research of a given functional equation is closely connected to property of stationary points of automorpism ω(z).
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| ISSN: | 0132-2818 2335-898X |