{"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.
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