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⊕Mb) = L(a) L(b) , where L is a complex-valued function defined on the complex unit disk. In the present article, we indicat...

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Main Authors:	Teerapong Suksumran, Keng Wiboonton
Format:	Journal
Published:	2018
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006489520&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57516
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-575162018-09-05T03:44:49Z Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk Teerapong Suksumran Keng Wiboonton Mathematics © 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⊕Mb) = 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. 2018-09-05T03:44:49Z 2018-09-05T03:44:49Z 2017-06-01 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/6653943832/57516
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Teerapong Suksumran Keng Wiboonton Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk
description	© 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⊕Mb) = 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.
format	Journal
author	Teerapong Suksumran Keng Wiboonton
author_facet	Teerapong Suksumran Keng Wiboonton
author_sort	Teerapong Suksumran
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	2018
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85006489520&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/57516
_version_	1681424893309091840

Möbius’s functional equation and Schur’s lemma with applications to the complex unit disk

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