{"title":"One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition","authors":"N. Kapustin, A. Kholomeeva","doi":"10.1134/s199508022460242x","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, we consider the spectral problem for the\nsemi-integer Bessel equation with a boundary condition containing\nthe square of the spectral parameter and a complex physical\nparameter. The system of eigenfunctions of the problem and the\ncharacteristic equation for the eigenvalues are derived. The\nequation for multiple roots of the characteristic equation is\nderived. The results on the basis properties (Riesz basis) of the\nsystem of eigenfunctions at different values of the parameter are\nobtained. For each case a biorthogonally conjugate system is\nconstructed. At the end of the paper there is an example for the\norder of Bessel functions equal to <span>\\(1/2\\)</span>.</p>","PeriodicalId":46135,"journal":{"name":"Lobachevskii Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Lobachevskii Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s199508022460242x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we consider the spectral problem for the
semi-integer Bessel equation with a boundary condition containing
the square of the spectral parameter and a complex physical
parameter. The system of eigenfunctions of the problem and the
characteristic equation for the eigenvalues are derived. The
equation for multiple roots of the characteristic equation is
derived. The results on the basis properties (Riesz basis) of the
system of eigenfunctions at different values of the parameter are
obtained. For each case a biorthogonally conjugate system is
constructed. At the end of the paper there is an example for the
order of Bessel functions equal to \(1/2\).
期刊介绍：
Lobachevskii Journal of Mathematics is an international peer reviewed journal published in collaboration with the Russian Academy of Sciences and Kazan Federal University. The journal covers mathematical topics associated with the name of famous Russian mathematician Nikolai Lobachevsky (Lobachevskii). The journal publishes research articles on geometry and topology, algebra, complex analysis, functional analysis, differential equations and mathematical physics, probability theory and stochastic processes, computational mathematics, mathematical modeling, numerical methods and program complexes, computer science, optimal control, and theory of algorithms as well as applied mathematics. The journal welcomes manuscripts from all countries in the English language.
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