多势能

摘要：

对于$\CC^n$的紧子集上的概率测度$μ$，我们定义了两个泛函$J(μ)$和$W(μ)$，它们是基于对$μ$和多元范德蒙德行列式的离散逼近建模的。我们发现，这些泛函相吻合，直到一个常数，与静电能量的$μ$定义在一个更一般的设置伯曼，Boucksom，Guedj和Zeriahi。这推广了复平面中测度的对数能量的经典概念;即，案例$n=1$。

英文摘要：

For probability measures $μ$ on compact subsets of $\CC^n$ we define two functionals $J(μ)$ and $W(μ)$ modeled on discrete approximations to $μ$ and multivariate Vandermonde determinants. We show that these functionals coincide, up to a constant, with the electrostatic energy of $μ$ defined in a more general setting by Berman, Boucksom, Guedj and Zeriahi. This generalizes the classical notion of logarithmic energy of a measure in the complex plane; i.e., the case $n=1$.

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。