{"title":"Growth of hypercyclic functions: a continuous path between -frequent hypercyclicity and hypercyclicity","authors":"Augustin Mouze, Vincent Munnier","doi":"10.1017/s0013091524000312","DOIUrl":null,"url":null,"abstract":"We are interested in the optimal growth in terms of <jats:italic>L<jats:sup>p</jats:sup></jats:italic>-averages of hypercyclic and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000312_inline2.png\"/> <jats:tex-math>$\\mathcal{U}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic functions on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" mimetype=\"image\" xlink:href=\"S0013091524000312_inline3.png\"/> <jats:tex-math>$\\mathcal{U}$</jats:tex-math> </jats:alternatives> </jats:inline-formula>-frequent hypercyclicity and hypercyclicity.","PeriodicalId":20586,"journal":{"name":"Proceedings of the Edinburgh Mathematical Society","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Edinburgh Mathematical Society","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000312","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We are interested in the optimal growth in terms of Lp-averages of hypercyclic and $\mathcal{U}$-frequently hypercyclic functions for some weighted Taylor shift operators acting on the space of analytic functions on the unit disc. We unify the results obtained by considering intermediate notions of upper frequent hypercyclicity between $\mathcal{U}$-frequent hypercyclicity and hypercyclicity.
期刊介绍：
The Edinburgh Mathematical Society was founded in 1883 and over the years, has evolved into the principal society for the promotion of mathematics research in Scotland. The Society has published its Proceedings since 1884. This journal contains research papers on topics in a broad range of pure and applied mathematics, together with a number of topical book reviews.
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