{"title":"Bounds for Eigenvalue Sums of Schrödinger Operators with Complex Radial Potentials","authors":"Jean-Claude Cuenin, Solomon Keedle-Isack","doi":"arxiv-2408.15783","DOIUrl":null,"url":null,"abstract":"We consider eigenvalue sums of Schr\\\"odinger operators $-\\Delta+V$ on\n$L^2(\\R^d)$ with complex radial potentials $V\\in L^q(\\R^d)$, $q<d$. We prove\nquantitative bounds on the distribution of the eigenvlaues in terms of the\n$L^q$ norm of $V$. A consequence of our bounds is that, if the eigenvlaues\n$(z_j)$ accumulates to a point in $(0,\\infty)$, then $(\\im z_j)$ is summable.\nThe key technical tools are resolvent estimates in Schatten spaces. We show\nthat these resolvent estimates follow from spectral measure estimates by an\nepsilon removal argument.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.15783","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We consider eigenvalue sums of Schr\"odinger operators $-\Delta+V$ on
$L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q
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