{"title":"连续谱中的积分态密度的规律性","authors":"M. Krishna","doi":"10.1007/s13226-024-00640-1","DOIUrl":null,"url":null,"abstract":"<p>In this paper we show that spectral measures of the Laplacian on <span>\\(\\ell ^2({\\mathbb {Z}}^d)\\)</span> are smooth in some regions of its spectrum, a result that extends to parts of the absolutely continuous spectrum of some random perturbations of it. The spectral measures considered are associated with dense sets of vectors.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"16 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Regularity of the integrated density of states in the continuous spectrum\",\"authors\":\"M. Krishna\",\"doi\":\"10.1007/s13226-024-00640-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we show that spectral measures of the Laplacian on <span>\\\\(\\\\ell ^2({\\\\mathbb {Z}}^d)\\\\)</span> are smooth in some regions of its spectrum, a result that extends to parts of the absolutely continuous spectrum of some random perturbations of it. The spectral measures considered are associated with dense sets of vectors.</p>\",\"PeriodicalId\":501427,\"journal\":{\"name\":\"Indian Journal of Pure and Applied Mathematics\",\"volume\":\"16 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Indian Journal of Pure and Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s13226-024-00640-1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00640-1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Regularity of the integrated density of states in the continuous spectrum
In this paper we show that spectral measures of the Laplacian on \(\ell ^2({\mathbb {Z}}^d)\) are smooth in some regions of its spectrum, a result that extends to parts of the absolutely continuous spectrum of some random perturbations of it. The spectral measures considered are associated with dense sets of vectors.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
