{"title":"由强m -椭圆伪微分算子生成的Lp(Rn)上有界线性算子的全纯单参数半群,1 < p < ∞","authors":"Yaodong Gao, M.W. Wong","doi":"10.1016/j.bulsci.2024.103535","DOIUrl":null,"url":null,"abstract":"<div><div>For a <em>M</em>-elliptic pseudo-differential operator on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we give a sufficient condition on its symbol to ensure that it is the infinitesimal generator of a holomorphic one-parameter semigroup of bounded linear operators on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span>.</div></div>","PeriodicalId":55313,"journal":{"name":"Bulletin des Sciences Mathematiques","volume":"198 ","pages":"Article 103535"},"PeriodicalIF":1.3000,"publicationDate":"2024-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Holomorphic one-parameter semigroups of bounded linear operators on Lp(Rn), 1 < p < ∞, generated by strongly M-elliptic pseudo-differential operators\",\"authors\":\"Yaodong Gao, M.W. Wong\",\"doi\":\"10.1016/j.bulsci.2024.103535\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For a <em>M</em>-elliptic pseudo-differential operator on <span><math><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup></math></span>, we give a sufficient condition on its symbol to ensure that it is the infinitesimal generator of a holomorphic one-parameter semigroup of bounded linear operators on <span><math><msup><mrow><mi>L</mi></mrow><mrow><mi>p</mi></mrow></msup><mo>(</mo><msup><mrow><mi>R</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span>, <span><math><mn>1</mn><mo><</mo><mi>p</mi><mo><</mo><mo>∞</mo></math></span>.</div></div>\",\"PeriodicalId\":55313,\"journal\":{\"name\":\"Bulletin des Sciences Mathematiques\",\"volume\":\"198 \",\"pages\":\"Article 103535\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-11-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin des Sciences Mathematiques\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0007449724001532\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin des Sciences Mathematiques","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0007449724001532","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Holomorphic one-parameter semigroups of bounded linear operators on Lp(Rn), 1 < p < ∞, generated by strongly M-elliptic pseudo-differential operators
For a M-elliptic pseudo-differential operator on , we give a sufficient condition on its symbol to ensure that it is the infinitesimal generator of a holomorphic one-parameter semigroup of bounded linear operators on , .