论具有特殊形式对数核的积分算子谱的渐近性

IF 0.8 4区数学 Q2 MATHEMATICS

Differential Equations Pub Date : 2023-12-01 DOI:10.1134/s0012266123120121

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引用次数: 0

摘要

摘要我们研究了一个积分算子频谱的渐近行为，该算子类似于一个具有对数核的积分算子，其对数核取决于参数之和。通过简单的变量变化，相应的方程被还原为定义在有限区间上的卷积型积分方程（众所周知，一般情况下此类方程无法通过二次方程求解）。接着，利用傅立叶变换，方程被简化为解析函数的共轭问题，然后又简化为一个无限线性代数方程组，通过分离其中的主要项，可以推导出确定原始问题频谱的关系。

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On Asymptotics of the Spectrum of an Integral Operator with a Logarithmic Kernel of a Special Form

Abstract

We study the asymptotic behavior of the spectrum of an integral operator similar to an integral operator with a logarithmic kernel depending on the sum of arguments. By a simple change of variables, the corresponding equation is reduced to an integral equation of convolution type defined on a finite interval (as is well known, such equations in the general case cannot be solved by quadratures). Next, using the Fourier transform, the equation is reduced to a conjugation problem for analytic functions and then to an infinite system of linear algebraic equations, the isolation of the main terms in which allows deriving a relation that determines the spectrum of the original problem.

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来源期刊

Differential Equations 数学-数学

CiteScore

1.30

自引率

33.30%

发文量

审稿时长

3-8 weeks

期刊介绍： Differential Equations is a journal devoted to differential equations and the associated integral equations. The journal publishes original articles by authors from all countries and accepts manuscripts in English and Russian. The topics of the journal cover ordinary differential equations, partial differential equations, spectral theory of differential operators, integral and integral–differential equations, difference equations and their applications in control theory, mathematical modeling, shell theory, informatics, and oscillation theory. The journal is published in collaboration with the Department of Mathematics and the Division of Nanotechnologies and Information Technologies of the Russian Academy of Sciences and the Institute of Mathematics of the National Academy of Sciences of Belarus.