{"title":"论波群的迹和势的规律性","authors":"Hart F. Smith","doi":"10.5802/aif.3538","DOIUrl":null,"url":null,"abstract":"For the wave equation $\\partial_t^2-\\Delta+V$ on $\\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\\rightarrow 0$ for the relative trace of the wave group.","PeriodicalId":50781,"journal":{"name":"Annales De L Institut Fourier","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the trace of the wave group and regularity of potentials\",\"authors\":\"Hart F. Smith\",\"doi\":\"10.5802/aif.3538\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the wave equation $\\\\partial_t^2-\\\\Delta+V$ on $\\\\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\\\\rightarrow 0$ for the relative trace of the wave group.\",\"PeriodicalId\":50781,\"journal\":{\"name\":\"Annales De L Institut Fourier\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales De L Institut Fourier\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.5802/aif.3538\",\"RegionNum\":4,\"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":"Annales De L Institut Fourier","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.5802/aif.3538","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the trace of the wave group and regularity of potentials
For the wave equation $\partial_t^2-\Delta+V$ on $\mathbb{R}^d$ with compactly supported, real valued potential $V$, we establish a sharp relation between Sobolev regularity of $V$ and the existence of finite order expansions as $t\rightarrow 0$ for the relative trace of the wave group.
期刊介绍:
The Annales de l’Institut Fourier aim at publishing original papers of a high level in all fields of mathematics, either in English or in French.
The Editorial Board encourages submission of articles containing an original and important result, or presenting a new proof of a central result in a domain of mathematics. Also, the Annales de l’Institut Fourier being a general purpose journal, highly specialized articles can only be accepted if their exposition makes them accessible to a larger audience.