{"title":"Lieb–Thirring inequalities on the spheres and SO(3)","authors":"André Kowacs, Michael Ruzhansky","doi":"10.1007/s13324-024-00991-2","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, we obtain new upper bounds for the Lieb–Thirring inequality on the spheres of any dimension greater than 2. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than 2. We also prove and exhibit an explicit new upper bound for the Lieb–Thirring inequality on <i>SO</i>(3). We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in <span>\\(L^2(\\mathbb {R}^n)\\)</span>, these inequalities have applications in quantum mechanics and other fields.</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00991-2","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we obtain new upper bounds for the Lieb–Thirring inequality on the spheres of any dimension greater than 2. As far as we have checked, our results improve previous results found in the literature for all dimensions greater than 2. We also prove and exhibit an explicit new upper bound for the Lieb–Thirring inequality on SO(3). We also discuss these estimates in the case of general compact Lie groups. Originally developed for estimating the sums of moments of negative eigenvalues of the Schrödinger operator in \(L^2(\mathbb {R}^n)\), these inequalities have applications in quantum mechanics and other fields.
期刊介绍:
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.