{"title":"超循环函数的增长：频繁超循环与超循环之间的连续路径","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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s0013091524000312\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s0013091524000312","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Growth of hypercyclic functions: a continuous path between -frequent hypercyclicity and hypercyclicity
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.
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