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

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 \(1/2\).

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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。

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来源期刊

Lobachevskii Journal of Mathematics MATHEMATICS-

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.