One Problem for the Bessel Equation with a Spectral Parameter in the Boundary Condition

IF 0.8 Q2 MATHEMATICS Lobachevskii Journal of Mathematics Pub Date : 2024-08-28 DOI:10.1134/s199508022460242x
N. Kapustin, A. Kholomeeva
{"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":"161 1","pages":""},"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 \(1/2\).

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
贝塞尔方程的一个问题,边界条件中有一个频谱参数
摘要 本文考虑了半整数贝塞尔方程的谱问题,其边界条件包含谱参数的平方和复物理参数。导出了问题的特征函数系和特征值的特征方程。得出了特征方程的多根方程。得出了不同参数值下特征函数系的基础性质(Riesz 基础)。针对每种情况,都构建了一个双对映共轭系统。在论文末尾有一个贝塞尔函数阶等于 \(1/2\)的例子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
CiteScore
1.50
自引率
42.90%
发文量
127
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.
期刊最新文献
Oscillations of Nanofilms in a Fluid Pressure Diffusion Waves in a Porous Medium Saturated by Three Phase Fluid Effect of a Rigid Cone Inserted in a Tube on Resonant Gas Oscillations Taylor Nearly Columnar Vortices in the Couette–Taylor System: Transition to Turbulence From Texts to Knowledge Graph in the Semantic Library LibMeta
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1