Abstract:The Maxwell operator is studied in a three-dimensional cylinder whose cross-section is a simply connected bounded domain with Lipschitz boundary. It is assumed that the coefficients of the operator are scalar functions depending on the longitudinal variable only. We show that the square of such an operator is unitarily equivalent to the orthogonal sum of four scalar elliptic operators of second order. If the coefficients are periodic along the axis of the cylinder, the spectrum of the Maxwell operator is absolutely continuous.

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中文翻译：

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圆柱体中的Maxwell算子的系数不依赖于横截面变量

摘要：在一个三维圆柱体中研究了麦克斯韦算子，该圆柱体的横截面是具有Lipschitz边界的简单连接的有界域。假定算子的系数是仅取决于纵向变量的标量函数。我们证明了这种算子的平方等于第二个四个标量椭圆算子的正交和。如果系数沿着圆柱轴是周期性的，则麦克斯韦算子的频谱是绝对连续的。

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