{"title":"Semiclassical functional calculus on nilpotent Lie groups and their compact nilmanifolds","authors":"Véronique Fischer, Søren Mikkelsen","doi":"arxiv-2409.05520","DOIUrl":null,"url":null,"abstract":"In this paper, we show that the semiclassical calculus recently developed on\nnilpotent Lie groups and nilmanifolds include the functional calculus of\nsuitable subelliptic operators. Moreover, we obtain Weyl laws for these\noperators. Amongst these operators are sub-Laplacians in horizontal divergence\nform perturbed with a potential and their generalisations.","PeriodicalId":501038,"journal":{"name":"arXiv - MATH - Representation Theory","volume":"36 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Representation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.05520","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we show that the semiclassical calculus recently developed on
nilpotent Lie groups and nilmanifolds include the functional calculus of
suitable subelliptic operators. Moreover, we obtain Weyl laws for these
operators. Amongst these operators are sub-Laplacians in horizontal divergence
form perturbed with a potential and their generalisations.
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