Abstract

In this paper, we are applied a new approach to prove that the solution of the linear Fredholm operator equation of the third kind given on a segment and having a finite number of multipoint singularities is equivalent to the solution of the linear Fredholm operator equation of the second kind with additional conditions. We are showed an example of solving the system of linear integral Fredholm equations of the third kind based on the equivalence of the above equations.

中文翻译：

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一类第三类线性Fredholm算子方程

摘要

在本文中，我们采用一种新方法来证明在一个段上给出的，具有有限个多点奇点的第三类线性Fredholm算子方程的解等于该线性Fredholm算子方程的解。第二种有附加条件。我们展示了一个基于上述方程的等价关系来求解第三类线性积分Fredholm方程组的示例。