{"title":"半经典子椭圆算子的参数","authors":"Hart F. Smith","doi":"10.2140/apde.2020.13.2375","DOIUrl":null,"url":null,"abstract":"We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix.","PeriodicalId":49277,"journal":{"name":"Analysis & PDE","volume":" ","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2020-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Parametrix for a semiclassical subelliptic operator\",\"authors\":\"Hart F. Smith\",\"doi\":\"10.2140/apde.2020.13.2375\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix.\",\"PeriodicalId\":49277,\"journal\":{\"name\":\"Analysis & PDE\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2020-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Analysis & PDE\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2140/apde.2020.13.2375\",\"RegionNum\":1,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis & PDE","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2140/apde.2020.13.2375","RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Parametrix for a semiclassical subelliptic operator
We demonstrate a parametrix construction, together with associated pseudodifferential operator calculus, for an operator of sum-of-squares type with semiclassical parameter. The form of operator we consider includes the generator of kinetic Brownian motion on the cosphere bundle of a Riemannian manifold. Regularity estimates in semiclassical Sobolev spaces are proven by establishing mapping properties for the parametrix.
期刊介绍：
APDE aims to be the leading specialized scholarly publication in mathematical analysis. The full editorial board votes on all articles, accounting for the journal’s exceptionally high standard and ensuring its broad profile.
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
