{"title":"带有傅里叶-诺伊曼展开的算子的谱分析","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":50654,"journal":{"name":"Complex Analysis and Operator Theory","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":50654,\"journal\":{\"name\":\"Complex Analysis and Operator Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-07-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Complex Analysis and Operator Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s11785-024-01577-3\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Complex Analysis and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s11785-024-01577-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Spectral Analysis of an Operator with Fourier-Neumann Expansions Beneath
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.
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Complex Analysis and Operator Theory (CAOT) is devoted to the publication of current research developments in the closely related fields of complex analysis and operator theory as well as in applications to system theory, harmonic analysis, probability, statistics, learning theory, mathematical physics and other related fields. Articles using the theory of reproducing kernel spaces are in particular welcomed.
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