{"title":"On the existence of eigenvalues of a one-dimensional Dirac operator","authors":"Daniel Sánchez-Mendoza, Monika Winklmeier","doi":"arxiv-2408.12697","DOIUrl":null,"url":null,"abstract":"The aim of this paper is to study the existence of eigenvalues in the gap of\nthe essential spectrum of the one-dimensional Dirac operator in the presence of\na bounded potential. We employ a generalized variational principle to prove\nexistence of such eigenvalues, estimate how many eigenvalues there are, and\ngive upper and lower bounds for them.","PeriodicalId":501373,"journal":{"name":"arXiv - MATH - Spectral Theory","volume":"18 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Spectral Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.12697","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
The aim of this paper is to study the existence of eigenvalues in the gap of
the essential spectrum of the one-dimensional Dirac operator in the presence of
a bounded potential. We employ a generalized variational principle to prove
existence of such eigenvalues, estimate how many eigenvalues there are, and
give upper and lower bounds for them.
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