薛定谔半群的Compactness
Compactness of Schrödinger semigroups
摘要：
本文研究了（在L^2-空间上）下有界的自伴算子扰动的本质谱的空性或半群的等价紧性。对于（非负）位势扰动，我们利用子水平集的特征函数乘算子的相对紧性，得到了半群紧性的一个简单判据.在狄利克雷形式的上下文中，我们甚至可以刻画测度扰动半群的紧性。在这里，某些“平均”的措施以外的紧凑集发挥作用。作为应用，我们得到了子级集在无穷远处薄的势的薛定谔算子半群的紧性。
英文摘要：
This paper is concerned with emptyness of the essential spectrum, or equivalently compactness of the semigroup, for perturbations of selfadjoint operators that are bounded below (on an L^2-space). For perturbations by a (nonnegative) potential we obtain a simple criterion for compactness of the semigroup in terms of relative compactness of the operators of multiplication with characteristic functions of sublevel sets. In the context of Dirichlet forms, we can even characterize compactness of the semigroup for measure perturbations. Here, certain 'averages' of the measure outside of compact sets play a role. As an application we obtain compactness of semigroups for Schrödinger operators with potentials whose sublevel sets are thin at infinity.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
