{"title":"ABSTRACT ALMOST PERIODICITY FOR GROUP ACTIONS ON UNIFORM TOPOLOGICAL SPACES","authors":"D. Lenz, Timo Spindeler, Nicolae Strungaru","doi":"10.4153/s0008414x23000226","DOIUrl":null,"url":null,"abstract":"We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action of a locally compact abelian group on a uniform topological space. We discuss the relation between Bohr and Bochner type almost periodicity, and similar conditions, and how the equivalence among such conditions relates to properties of the group action and the uniformity. We complete the paper by demonstrating how various examples considered earlier all fit in our framework.","PeriodicalId":55284,"journal":{"name":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","volume":"69 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2022-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Mathematics-Journal Canadien De Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4153/s0008414x23000226","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We present a unified theory for the almost periodicity of functions with values in an arbitrary Banach space, measures and distributions via almost periodic elements for the action of a locally compact abelian group on a uniform topological space. We discuss the relation between Bohr and Bochner type almost periodicity, and similar conditions, and how the equivalence among such conditions relates to properties of the group action and the uniformity. We complete the paper by demonstrating how various examples considered earlier all fit in our framework.
期刊介绍：
The Canadian Journal of Mathematics (CJM) publishes original, high-quality research papers in all branches of mathematics. The Journal is a flagship publication of the Canadian Mathematical Society and has been published continuously since 1949. New research papers are published continuously online and collated into print issues six times each year.
To be submitted to the Journal, papers should be at least 18 pages long and may be written in English or in French. Shorter papers should be submitted to the Canadian Mathematical Bulletin.
Le Journal canadien de mathématiques (JCM) publie des articles de recherche innovants de grande qualité dans toutes les branches des mathématiques. Publication phare de la Société mathématique du Canada, il est publié en continu depuis 1949. En ligne, la revue propose constamment de nouveaux articles de recherche, puis les réunit dans des numéros imprimés six fois par année.
Les textes présentés au JCM doivent compter au moins 18 pages et être rédigés en anglais ou en français. C’est le Bulletin canadien de mathématiques qui reçoit les articles plus courts.
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