Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
Boundary triplets and M -functions for non-selfadjoint operators, with applications to elliptic PDEs and block operator matrices
复制标题
非自共轭算子的边界三元组和 M 函数，及其在椭圆偏微分方程和块算子矩阵中的应用
DOI：
10.1112/jlms/jdn006
复制
发表时间：
2008
期刊：
影响因子：
--
通讯作者：
Brown M
中科院分区：
文献类型：
--
作者：
Brown M
从一个伴随算子对开始，在标准PDE假设的适当抽象版本下，我们考虑算子扩展的WeylM-函数。的扩展是由抽象的边界条件，我们建立的结果之间的关系theM-函数作为一个解析函数的谱参数和频谱的扩展。我们还给出了M-函数不包含预解式的全部谱信息的例子，并证明了所得结果可应用于M-函数对应于Dirichlet到Neumann映射的椭圆型偏微分方程.
Starting with an adjoint pair of operators, under suitable abstract versions of standard PDE hypotheses, we consider the WeylM-function of extensions of the operators. The extensions are determined by abstract boundary conditions and we establish results on the relationship between theM-function as an analytic function of a spectral parameter and the spectrum of the extension. We also give an example where theM-function does not contain the whole spectral information of the resolvent, and show that the results can be applied to elliptic PDEs where theM-function corresponds to the Dirichlet to Neumann map.