Transfinite Diameter, Chebyshev Constant and Energy on Locally Compact Spaces
Transfinite Diameter, Chebyshev Constant and Energy on Locally Compact Spaces
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局部紧空间上的超限直径、切比雪夫常数和能量
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
B. Nagy
中科院分区：
文献类型：
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作者：
B. Farkas;B. Nagy
本文在Choquet、Fuglede和Ohtsuka开创的抽象线性势分析的基础上，研究了超有限直径、切比雪夫常数和Wiener能量之间的关系。事实证明，只要势理论核满足最大值原理，那么所有这些量对所有紧集都是相等的。对于连续核，甚至匡威的陈述也是正确的：如果任何紧集的切比雪夫常数与其超限直径一致，则核必须满足最大值原理。提供了大量的例子来显示结果的清晰度。
We study the relationship between transfinite diameter, Chebyshev constant and Wiener energy in the abstract linear potential analytic setting pioneered by Choquet, Fuglede and Ohtsuka. It turns out that, whenever the potential theoretic kernel satisfies the maximum principle, then all these quantities are equal for all compact sets. For continuous kernels even the converse statement is true: if the Chebyshev constant of any compact set coincides with its transfinite diameter, the kernel must satisfy the maximum principle. An abundance of examples is provided to show the sharpness of the results.