论文标题
光谱部分
Spectral Sections
论文作者
论文摘要
该论文致力于梅尔罗斯和广场引入的光谱部分的概念。在本文的第一部分中，我们将梅尔罗斯和广场的结果推广到任意基础空间，不一定是紧凑的。第二部分包含许多应用程序，包括用于通过非紧密基础空间参数参数的Dirac类型运算符家族的COBORDISM定理。在本文的第三部分中，我们研究了Riesz的连续性对于存在光谱部分还是广义频谱部分是必需的。特别是，我们表明，如果具有紧凑型分解的常规自我接合算子的映射家族具有光谱部分，那么该家族是Riesz的连续。
The paper is devoted to the notion of a spectral section introduced by Melrose and Piazza. In the first part of the paper we generalize results of Melrose and Piazza to arbitrary base spaces, not necessarily compact. The second part contains a number of applications, including cobordism theorems for families of Dirac type operators parametrized by a non-compact base space. In the third part of the paper we investigate whether Riesz continuity is necessary for existence of a spectral section or a generalized spectral section. In particular, we show that if a graph continuous family of regular self-adjoint operators with compact resolvents has a spectral section, then the family is Riesz continuous.
