{"title":"具有复径向势的薛定谔算子特征值和的界限","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":"{\"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}","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}