{"title":"分数拉普拉斯生成的解析半群的边界值","authors":"Chung-Sik Sin","doi":"10.1007/s00013-024-02004-x","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, using the theory of boundary values of analytic semigroups, we find necessary and sufficient conditions to guarantee that the operator <span>\\(i(-\\Delta )^{{\\alpha }/{2}}\\)</span> generates a strongly continuous semigroup in <span>\\(L^p(\\mathbb {R}^n)\\)</span>.</p></div>","PeriodicalId":8346,"journal":{"name":"Archiv der Mathematik","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Boundary values of analytic semigroups generated by fractional Laplacians\",\"authors\":\"Chung-Sik Sin\",\"doi\":\"10.1007/s00013-024-02004-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present paper, using the theory of boundary values of analytic semigroups, we find necessary and sufficient conditions to guarantee that the operator <span>\\\\(i(-\\\\Delta )^{{\\\\alpha }/{2}}\\\\)</span> generates a strongly continuous semigroup in <span>\\\\(L^p(\\\\mathbb {R}^n)\\\\)</span>.</p></div>\",\"PeriodicalId\":8346,\"journal\":{\"name\":\"Archiv der Mathematik\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2024-05-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Archiv der Mathematik\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-02004-x\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Archiv der Mathematik","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-02004-x","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Boundary values of analytic semigroups generated by fractional Laplacians
In the present paper, using the theory of boundary values of analytic semigroups, we find necessary and sufficient conditions to guarantee that the operator \(i(-\Delta )^{{\alpha }/{2}}\) generates a strongly continuous semigroup in \(L^p(\mathbb {R}^n)\).
期刊介绍：
Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.
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