C^N中的超限直径概念与范德蒙德行列式的积分
Transfinite diameter notions in C^N and integrals of Vandermonde determinants
摘要：
我们提供了一个一般的框架，并指出超限直径，齐次超限直径和加权超限直径的概念之间的关系在C^N。一个成分是Rumely公式，它将Robin函数与紧集的超限直径联系起来。对于C^N中的一般紧集和测度，我们还证明了广义变权范德蒙德行列式积分的极限公式.我们的结果推广到定义在R^N中锥上的某些权和测度。
英文摘要：
We provide a general framework and indicate relations between the notions of transfinite diameter, homogeneous transfinite diameter, and weighted transfinite diameter for sets in C^N. An ingredient is a formula of Rumely which relates the Robin function and the transfinite diameter of a compact set. We also prove limiting formulas for integrals of generalized Vandermonde determinants with varying weights for a general class of compact sets and measures in C^N. Our results extend to certain weights and measures defined on cones in R^N.
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。
