论文标题
Neumann-Poincaré操作员在旋转对称结构域中的光谱特性
Spectral properties of the Neumann-Poincaré operator on rotationally symmetric domains in two dimensions
论文作者
论文摘要
本文涉及Neumann-Poincaré操作员在$ m $折的旋转对称平面域上的光谱特性。 $ m $折叠的旋转对称性简单连接域$ d $被视为某个域的$ m $ th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-th-brot变换。我们证明，$ D $上的Neumann-Poincaré运算符定义的域被分解为不变子空间，其中一个频谱是$ω$上的Spectrum的确切副本。它特别意味着转换域上的频谱$ d $包含原始域$ω$计数倍数的频谱。
This paper concerns the spectral properties of the Neumann-Poincaré operator on $m$-fold rotationally symmetric planar domains. An $m$-fold rotationally symmetric simply connected domain $D$ is realized as the $m$th-root transform of a certain domain, say $Ω$. We prove that the domain of definition of the Neumann-Poincaré operator on $D$ is decomposed into invariant subspaces and the spectrum on one of them is the exact copy of the spectrum on $Ω$. It implies in particular that the spectrum on the transformed domain $D$ contains the spectrum on the original domain $Ω$ counting multiplicities.
