{"title":"Recovering the Shape of an Equilateral Quantum Tree by Two Spectra","authors":"Vyacheslav Pivovarchik","doi":"10.1007/s00020-024-02759-6","DOIUrl":null,"url":null,"abstract":"<p>We show how to find the shape of an equilateral tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm–Liouville equation. In case of snowflake trees the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree.</p>","PeriodicalId":13658,"journal":{"name":"Integral Equations and Operator Theory","volume":"2010 1","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2024-03-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Integral Equations and Operator Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00020-024-02759-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show how to find the shape of an equilateral tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm–Liouville equation. In case of snowflake trees the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree.
期刊介绍：
Integral Equations and Operator Theory (IEOT) is devoted to the publication of current research in integral equations, operator theory and related topics with emphasis on the linear aspects of the theory. The journal reports on the full scope of current developments from abstract theory to numerical methods and applications to analysis, physics, mechanics, engineering and others. The journal consists of two sections: a main section consisting of refereed papers and a second consisting of short announcements of important results, open problems, information, etc.
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