{"title":"Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath","authors":"Krzysztof Stempak","doi":"10.1007/s11785-024-01577-3","DOIUrl":null,"url":null,"abstract":"<p>We perform spectral analysis of a Sturm-Liouville operator on <span>\\(L^2(\\mathbb {R}_+,dx)\\)</span> which, through the Liouville transformation, is unitarily equivalent to the Schrödinger operator on <span>\\(L^2(\\mathbb {R},dx)\\)</span> with heavy negative potential <span>\\(V(x)=-e^{2x}\\)</span>. This analysis clarifies some operator theory aspects of the setting of Fourier-Neumann expansions initiated by Varona in 1994. </p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01577-3","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
We perform spectral analysis of a Sturm-Liouville operator on \(L^2(\mathbb {R}_+,dx)\) which, through the Liouville transformation, is unitarily equivalent to the Schrödinger operator on \(L^2(\mathbb {R},dx)\) with heavy negative potential \(V(x)=-e^{2x}\). This analysis clarifies some operator theory aspects of the setting of Fourier-Neumann expansions initiated by Varona in 1994.