Abstract

It is studied a regularization of systems of linear Volterra integral equations of the third kind with continuous kernel degenerated at points of the given segment on the diagonal. The determinant of the matrix outside the integral disappears at the starting point or at the end of the segment. Regularizing Lavrent’ev type operator is constructed that preserves the property of Volterra equation. It is proved the uniform convergence of the regularized solution to the exact solution, and defined the conditions of uniqueness of the solution in the Hölder space. Also it is considered the case of systems of third kind Volterra linear integral equations with the approximated right hand side of equation. It is established conditions under which a regularized solution of the equation with approximately given right-hand side can serve as an approximate solution to the original equation.

中文翻译：

---

第三类Volterra线性积分方程组的正则化。

摘要

研究了第三类线性Volterra积分方程组的正则化，其中在对角线上给定线段的点上具有连续的核。积分之外的矩阵的行列式在线段的起点或终点消失。构造正则化Lavrent'ev类型算子，该算子保留了Volterra方程的性质。证明了正则化解与精确解的一致收敛，并定义了Hölder空间中解唯一性的条件。还考虑了第三类Volterra线性积分方程组的情况，其中方程的右侧近似。