论文标题
奇异派对 - 迪克的光谱渐近性和积极性
Spectral asymptotic and positivity for singular Dirichlet-to-Neumann operators
论文作者
论文摘要
在希尔伯特（Hilbert）空间的框架内，我们将提供必要的足够条件，以通过Dirichlet原理定义Dirichlet到Neumann操作员。对于奇异的dirichlet到Neumann运营商，我们将建立近乎奇异性的劳伦（Laurent）扩展，以及leffler的扩展，以扩展相关的二次形式。既定的结果将被利用，以确切地解决$ l^2 $设置中相关半群的积极性问题。获得的结果得到了Lipschitz域上的一些示例支持。除其他结果外，我们将证明边界的规律性可能会影响阳性，并为单数Dirichlet到Neumann运算符的特征值提供Mittag-Leffler的扩展。
In the framework of Hilbert spaces we shall give necessary and sufficient conditions to define a Dirichlet-to-Neumann operator via Dirichlet principle. For singular Dirichlet-to-Neumann operators we will establish Laurent expansion near singularities as well as Mittag--Leffler expansion for the related quadratic form. The established results will be exploited to solve definitively the problem of positivity of the related semigroup in the $L^2$ setting. The obtained results are supported by some examples on Lipschitz domains. Among other results, we shall demonstrate that regularity of the boundary may affect positivity and derive Mittag-Leffler expansion for the eigenvalues of singular Dirichlet-to-Neumann operators.
