度量缺失时正积分算子的可迹性
Traceability of positive integral operators in the absence of a metric
摘要：
当$X$是Hausdorff局部紧的第二可数空间，$μ$是非退化的、$σ$ -有限的和局部有限的Borel测度时，研究了正积分算子在$L^2(X,μ)$上的可溯性.这种设置包括其他情况下证明的文献中，例如其中$X$是一个紧凑的度量空间和$μ$是一个特殊的有限措施。结果适用于球，环面和其他相关的子集通常的空间$\mathbb{R}^m$。
英文摘要：
We investigate the traceability of positive integral operators on $L^2(X,μ)$ when $X$ is a Hausdorff locally compact second countable space and $μ$ is a non-degenerate, $σ$-finite and locally finite Borel measure. This setting includes other cases proved in the literature, for instance the one in which $X$ is a compact metric space and $μ$ is a special finite measure. The results apply to spheres, tori and other relevant subsets of the usual space $\mathbb{R}^m$.
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。
