{"title":"一般零豪斯多夫谱测度和单填充谱测度","authors":"S. L. Carvalho, C. R. de Oliveira","doi":"10.1063/1.5141763","DOIUrl":null,"url":null,"abstract":"For some metric spaces of self-adjoint operators, it is shown that the set of operators whose spectral measures have simultaneously zero upper-Hausdorff and one lower-packing dimensions contains a dense $G_\\delta$ subset. Applications include sets of limit-periodic operators.","PeriodicalId":8426,"journal":{"name":"arXiv: Functional Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Generic zero-Hausdorff and one-packing spectral measures\",\"authors\":\"S. L. Carvalho, C. R. de Oliveira\",\"doi\":\"10.1063/1.5141763\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For some metric spaces of self-adjoint operators, it is shown that the set of operators whose spectral measures have simultaneously zero upper-Hausdorff and one lower-packing dimensions contains a dense $G_\\\\delta$ subset. Applications include sets of limit-periodic operators.\",\"PeriodicalId\":8426,\"journal\":{\"name\":\"arXiv: Functional Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Functional Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1063/1.5141763\",\"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: Functional Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1063/1.5141763","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Generic zero-Hausdorff and one-packing spectral measures
For some metric spaces of self-adjoint operators, it is shown that the set of operators whose spectral measures have simultaneously zero upper-Hausdorff and one lower-packing dimensions contains a dense $G_\delta$ subset. Applications include sets of limit-periodic operators.
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