{"title":"算子半群的遍历性与弱混合的等价性","authors":"M. Hmissi, F. Mokchaha","doi":"10.12732/ijam.v36i2.1","DOIUrl":null,"url":null,"abstract":": We prove the equivalence between ergodicity and weak mixing of an invariant probability measure m for strongly continuous contraction semigroups of linear operators on L 2 ( m ) satisfying the sector condition. The same result is proved for subordinated semigroups in the Bochner sense by the one-sided stable sudordinators","PeriodicalId":312472,"journal":{"name":"International Journal of Apllied Mathematics","volume":"44 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-05-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"ON THE EQUIVALENCE BETWEEN ERGODICITY AND WEAK MIXING FOR OPERATORS SEMIGROUPS\",\"authors\":\"M. Hmissi, F. Mokchaha\",\"doi\":\"10.12732/ijam.v36i2.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\": We prove the equivalence between ergodicity and weak mixing of an invariant probability measure m for strongly continuous contraction semigroups of linear operators on L 2 ( m ) satisfying the sector condition. The same result is proved for subordinated semigroups in the Bochner sense by the one-sided stable sudordinators\",\"PeriodicalId\":312472,\"journal\":{\"name\":\"International Journal of Apllied Mathematics\",\"volume\":\"44 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-05-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Apllied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/ijam.v36i2.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Apllied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/ijam.v36i2.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
ON THE EQUIVALENCE BETWEEN ERGODICITY AND WEAK MIXING FOR OPERATORS SEMIGROUPS
: We prove the equivalence between ergodicity and weak mixing of an invariant probability measure m for strongly continuous contraction semigroups of linear operators on L 2 ( m ) satisfying the sector condition. The same result is proved for subordinated semigroups in the Bochner sense by the one-sided stable sudordinators
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