Abstract

Integral representations of solutions of one differential equation with singularities in the coefficients, containing the Bessel operator perturbed by some potential, are considered. The existence of integral representations of a certain type for such solutions is proved by the method of successive approximations using transform operators. Potentials with strong singularities at the origin are allowed. As compared with the known results, the Riemann function is expressed not via the general hypergeometric function, but, more specifically, via the Legendre function, which helps to avoid unknown constants in the estimates.

中文翻译：

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关于变换算子理论中的一个积分方程

摘要

考虑一个微分方程的解的积分表示，该微分方程的系数具有奇异性，其中包含被某些电位扰动的贝塞尔算子。通过使用变换算子的逐次逼近方法，证明了此类解决方案具有某种类型的积分表示形式。允许在原点处具有很强的奇点的电势。与已知结果相比，Riemann函数不是通过一般的超几何函数表示的，而是通过Legendre函数表示的，这有助于避免估计中的未知常数。