Chaos for Cosine Operator Functions on Groups

Let 1≤p<∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simult...

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Main Author: Chung-Chuan Chen
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/603234
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author Chung-Chuan Chen
author_facet Chung-Chuan Chen
author_sort Chung-Chuan Chen
collection DOAJ
description Let 1≤p<∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.
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spelling doaj-art-b97d6bfd8cb34a7f9ce6402c2a0bda6f2025-02-03T05:53:55ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/603234603234Chaos for Cosine Operator Functions on GroupsChung-Chuan Chen0Department of Mathematics Education, National Taichung University of Education, Taichung 403, TaiwanLet 1≤p<∞ and G be a locally compact group. We characterize chaotic cosine operator functions, generated by weighted translations on the Lebesgue space Lp(G), in terms of the weight condition. In particular, chaotic cosine operator functions and chaotic weighted translations can only occur simultaneously. We also give a necessary and sufficient condition for the direct sum of a sequence of cosine operator functions to be chaotic.http://dx.doi.org/10.1155/2014/603234
spellingShingle Chung-Chuan Chen
Chaos for Cosine Operator Functions on Groups
Abstract and Applied Analysis
title Chaos for Cosine Operator Functions on Groups
title_full Chaos for Cosine Operator Functions on Groups
title_fullStr Chaos for Cosine Operator Functions on Groups
title_full_unstemmed Chaos for Cosine Operator Functions on Groups
title_short Chaos for Cosine Operator Functions on Groups
title_sort chaos for cosine operator functions on groups
url http://dx.doi.org/10.1155/2014/603234
work_keys_str_mv AT chungchuanchen chaosforcosineoperatorfunctionsongroups