局部紧空间中凝聚子的内容
Interior capacities of condensers in locally compact spaces
摘要：
这项研究的动机是已知的事实，即在非紧的情况下，在局部紧空间中的凝聚器内部容量理论的主要最小问题通常是不可解的，即使在非常自然的假设下也会发生这种情况（例如，对于欧几里得空间和闭凝聚器中的牛顿、格林或里斯核）。因此，特别有趣的是，找到与主极小问题对偶的变分问题的陈述（并因此提供了容量的一些新的等价定义），但总是可解的（例如，即使对于非封闭式冷凝器也是如此）。正定核满足B. Fuglede的条件之间的强和淡拓扑的一致性，问题所需的性质提出并解决。他们的解决方案提供了一个自然的推广，著名的概念，内部容性分布与一组。我们给出了这些解决方案的描述，建立他们的唯一性和连续性的声明，并指出他们的特征属性。凝聚器被视为任意集合的有限集合，其中sing +1或-1被指定，使得相反符号集合的闭包相互不相交。
英文摘要：
The study is motivated by the known fact that, in the noncompact case, the main minimum-problem of the theory of interior capacities of condensers in a locally compact space is in general unsolvable, and this occurs even under very natural assumptions (e.g., for the Newton, Green, or Riesz kernels in an Euclidean space and closed condensers). Therefore it was particularly interesting to find statements of variational problems dual to the main minimum-problem (and hence providing some new equivalent definitions of the capacity), but always solvable (e.g., even for nonclosed condensers). For all positive definite kernels satisfying B. Fuglede's condition of consistency between the strong and vague topologies, problems with the desired properties are posed and solved. Their solutions provide a natural generalization of the well-known notion of interior capacitary distributions associated with a set. We give a description of those solutions, establish statements on their uniqueness and continuity, and point out their characteristic properties. A condenser is treated as a finite collection of arbitrary sets with sing +1 or -1 prescribed, such that the closures of opposite-signed sets are mutually disjoint.
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。
