Abstract

A linear second-order hyperbolic equation of two independent variables with a singular Bessel operator is considered. For particular types of such equations, a detailed literature review of known methods for constructing Riemann functions is given. It is shown that to construct the Riemann function for equations with a singular Bessel operator, we can use the Erdélyi–Kober transmutation operator. The Riemann function for the Euler–Poisson–Darboux differential equations is found in explicit form. In this paper, we give examples and an algorithm for constructing the Riemann function for second-order hyperbolic equations with the Bessel operator.

中文翻译：

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用奇异贝塞尔算子构造偏微分方程的黎曼函数的方法

摘要

考虑具有奇异贝塞尔算子的两个自变量的线性二阶双曲方程。对于这类方程式的特定类型，给出了有关构造黎曼函数的已知方法的详细文献综述。结果表明，要用奇异的Bessel算子构造方程的Riemann函数，我们可以使用Erdélyi-Kober变换算子。Euler–Poisson–Darboux微分方程的Riemann函数以显式形式发现。在本文中，我们给出了使用Bessel算子构造二阶双曲方程的Riemann函数的示例和算法。