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

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

引用次数: 0

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.

查看原文

论具有特殊形式对数核的积分算子谱的渐近性

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。

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分钟内获得全文求助全文