Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk
| Autor: | Keng Wiboonton, Teerapong Suksumran |
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| Rok vydání: | 2016 |
| Předmět: |
Discrete mathematics
Lemma (mathematics) Pure mathematics Mathematics::Combinatorics Mathematics::Number Theory Applied Mathematics General Mathematics 010102 general mathematics Schur's lemma Structure (category theory) Cauchy distribution 010103 numerical & computational mathematics Function (mathematics) 01 natural sciences Unit disk Exponential function Functional equation Discrete Mathematics and Combinatorics 0101 mathematics Mathematics |
| Zdroj: | Aequationes mathematicae. 91:491-503 |
| ISSN: | 1420-8903 0001-9054 |
| DOI: | 10.1007/s00010-016-0452-9 |
| Popis: | Mobius addition is defined on the complex open unit disk by $$\begin{aligned} a\oplus _M b = \dfrac{a+b}{1+\bar{a}b} \end{aligned}$$ and Mobius’s exponential equation takes the form $$L(a\oplus _M b) = L(a)L(b)$$ , where L is a complex-valued function defined on the complex unit disk. In the present article, we indicate how Mobius’s exponential equation is connected to Cauchy’s exponential equation. Mobius’s exponential equation arises when one determines the irreducible linear representations of the unit disk equipped with Mobius addition, considered as a nonassociative group-like structure. This suggests studying Schur’s lemma in a more general setting. |
| Databáze: | OpenAIRE |
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