Abstract

A vector problem of electromagnetic-wave diffraction by a cylinder is described by a system of two two-dimensional integro-differential equations. After expanding the unknown functions and the right-hand sides in Fourier series, the problem reduces to systems of one-dimensional equations. Analytical inversion of the principal operator of one-dimensional systems in Sobolev spaces is considered. Theorems on the boundedness and bounded invertibility of the principal operator are proved. The inverse operator is represented by series and in closed form: the elements of the inverse matrix are integral or integro-differential operators.

中文翻译：

---

Sobolev空间中圆柱段衍射问题的算符矩阵的解析求逆。

摘要

用两个二维积分微分方程组描述圆柱体进行电磁波衍射的矢量问题。在扩展了傅立叶级数中的未知函数和右手边后，该问题简化为一维方程组。考虑了Sobolev空间中一维系统的主算符的解析反演。证明了关于主算子的有界性和有界可逆性的定理。逆算子由序列和封闭形式表示：逆矩阵的元素是整数或整数微分算子。