The Essential Spectrum of the Neumann–Poincaré Operator on a Domain with Corners
The Essential Spectrum of the Neumann–Poincaré Operator on a Domain with Corners
复制标题
带角域上诺依曼-庞加莱算子的本征谱
DOI：
10.1007/s00205-016-1051-6
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发表时间：
2016
影响因子：
2.5
通讯作者：
M. Putinar
中科院分区：
文献类型：
--
作者：
Karl;M. Putinar
利用复平面中楔形的齐次结构，我们计算了作用于相关Bergman空间的反线性Ahlfors-Beurling变换的谱。因此，Ahlfors-Beurling变换与neumann - poincarcarr算子之间的相似等价提供了后者在楔形上的积分算子的谱。利用局域化技术和保角映射，第一次完整地描述了具有角的平面域上neumann - poincar<s:1>算子的基本谱与相关谐波场的能量范数的关系。
Exploiting the homogeneous structure of a wedge in the complex plane, we compute the spectrum of the anti-linear Ahlfors–Beurling transform acting on the associated Bergman space. Consequently, the similarity equivalence between the Ahlfors–Beurling transform and the Neumann–Poincaré operator provides the spectrum of the latter integral operator on a wedge. A localization technique and conformal mapping lead to the first complete description of the essential spectrum of the Neumann–Poincaré operator on a planar domain with corners, with respect to the energy norm of the associated harmonic field.