{"title":"Schrödinger半群的范畴定理","authors":"M. Aloisio, S. L. Carvalho, C. Oliveira","doi":"10.4171/zaa/1666","DOIUrl":null,"url":null,"abstract":"Stimulated by the category theorems of Eisner and Ser\\'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr\\\"odinger semigroups. Specifically, we show that, to a given class of Schr\\\"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr\\\"{o}dinger operators.","PeriodicalId":54402,"journal":{"name":"Zeitschrift fur Analysis und ihre Anwendungen","volume":" ","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2019-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Category Theorems for Schrödinger Semigroups\",\"authors\":\"M. Aloisio, S. L. Carvalho, C. Oliveira\",\"doi\":\"10.4171/zaa/1666\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Stimulated by the category theorems of Eisner and Ser\\\\'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr\\\\\\\"odinger semigroups. Specifically, we show that, to a given class of Schr\\\\\\\"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr\\\\\\\"{o}dinger operators.\",\"PeriodicalId\":54402,\"journal\":{\"name\":\"Zeitschrift fur Analysis und ihre Anwendungen\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2019-02-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Zeitschrift fur Analysis und ihre Anwendungen\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/zaa/1666\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Zeitschrift fur Analysis und ihre Anwendungen","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/zaa/1666","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Stimulated by the category theorems of Eisner and Ser\'eny in the setting of unitary and isometric $C_0$-semigroups on separable Hilbert spaces, we prove category theorems for Schr\"odinger semigroups. Specifically, we show that, to a given class of Schr\"{o}dinger semigroups, Baire generically the semigroups are strongly stable but not exponentially stable. We also present a typical spectral property of the corresponding Schr\"{o}dinger operators.
期刊介绍：
The Journal of Analysis and its Applications aims at disseminating theoretical knowledge in the field of analysis and, at the same time, cultivating and extending its applications.
To this end, it publishes research articles on differential equations and variational problems, functional analysis and operator theory together with their theoretical foundations and their applications – within mathematics, physics and other disciplines of the exact sciences.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
