Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk
© 2016, Springer International Publishing. Möbius addition is defined on the complex open unit disk by (Formula presented.) and Möbius’s exponential equation takes the form L(a⊕ M b) = L(a) L(b) , where L is a complex-valued function defined on the complex unit disk. In the present article, we indi...
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th-cmuir.6653943832-403972017-09-28T04:09:21Z Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk Suksumran T. Wiboonton K. © 2016, Springer International Publishing. Möbius addition is defined on the complex open unit disk by (Formula presented.) and Möbius’s exponential equation takes the form L(a⊕ 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 Möbius’s exponential equation is connected to Cauchy’s exponential equation. Möbius’s exponential equation arises when one determines the irreducible linear representations of the unit disk equipped with Möbius addition, considered as a nonassociative group-like structure. This suggests studying Schur’s lemma in a more general setting. 2017-09-28T04:09:21Z 2017-09-28T04:09:21Z 3 Journal 00019054 2-s2.0-85006489520 10.1007/s00010-016-0452-9 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006489520&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40397 |
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© 2016, Springer International Publishing. Möbius addition is defined on the complex open unit disk by (Formula presented.) and Möbius’s exponential equation takes the form L(a⊕ 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 Möbius’s exponential equation is connected to Cauchy’s exponential equation. Möbius’s exponential equation arises when one determines the irreducible linear representations of the unit disk equipped with Möbius addition, considered as a nonassociative group-like structure. This suggests studying Schur’s lemma in a more general setting. |
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Journal |
| author |
Suksumran T. Wiboonton K. |
| spellingShingle |
Suksumran T. Wiboonton K. Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| author_facet |
Suksumran T. Wiboonton K. |
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Suksumran T. |
| title |
Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| title_short |
Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| title_full |
Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| title_fullStr |
Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| title_full_unstemmed |
Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk |
| title_sort |
möbius’s functional equation and schur’s lemma with applications to the complex unit disk |
| publishDate |
2017 |
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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006489520&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40397 |
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