发表机构
Institute of Science and Technology Austria; Graz University of Technology（IST奥地利科学与技术研究所; 格拉茨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究加权空间中带增性势的薛定谔算子，给出预解集非空、定义域分离及预解紧性与Schatten类条件，并推广特征系统完备性至加权空间，应用于强增性阻尼波动方程。
AI 中文摘要
我们在加权空间中分析具有增性势的薛定谔算子。我们找到了势和权重的条件，在这些条件下，通过广义形式方法引入的Dirichlet实现具有非空预解集。我们建立了定义域和图像范数的分离性质，以及预解算子的紧性和Schatten类的充分条件。此外，我们研究了标准空间和加权空间中算子的离散谱与特征函数之间的关系。作为应用，我们将具有增性势的算子的特征系统完备性结果从标准空间推广到加权空间，并分析了表现出Schur支配性质的算子矩阵，特别是与具有强增性阻尼的波动方程相关的算子矩阵。
英文摘要
We analyse Schrödinger operators with accretive potentials in weighted spaces. We find conditions on potentials and weights for which the Dirichlet realisation, introduced by generalised form methods, has non-empty resolvent set. We establish a domain and graph norm separation property, as well as sufficient conditions for the compactness and Schatten class of the resolvent. Moreover, we investigate the relation between discrete spectra and eigenfunctions of operators in standard and weighted spaces. As applications we extend results on the completeness of eigensystems of operators with accretive potentials from standard to weighted spaces and analyse operator matrices exhibiting a Schur dominance property, in particular, related to a wave equation with strong accretive damping.
Comments45 pages
