{"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}
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Abstract
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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