Fekete-Leja超限直径的Robin公式

具有广义多项式次数的超限直径

Transfinite diameter with generalized polynomial degree

本文针对广义多项式次数定义的加权超限直径，证明了切比雪夫变换公式，并将Leja点推广到该框架，进而证明无权情形下广义Leja点可恢复超限直径。

Pade interpolation by F-polynomials and transfinite diameter

We define $F$-polynomials as linear combinations of dilations by some frequencies of an entire function $F$. In this paper we use Pade interpolation of holomorphic functions in the unit disk by $F$-polynomials to obtain explicitly approximating $F$-polynomials with sharp estimates on their coefficients. We show that when frequencies lie in a compact set $K\subset\mathbb C$ then optimal choices for the frequencies of interpolating polynomials are similar to Fekete points. Moreover, the minimal norms of the interpolating operators form a sequence whose rate of growth is determined by the transfi…

Transfinite diameter on complex algebraic varieties

We use methods from computational algebraic geometry to study Chebyshev constants and the transfinite diameter of a pure $m$-dimensional affine algebraic variety in $\mathbb{C}^n$ ($m\leq n$). The main result is a generalization of Zaharjuta's integral formula for the Fekete-Leja transfinite diameter.

多维伪Leja序列

Multidimensional pseudo-Leja sequences

本文提出多维伪Leja序列的定义，推广了一维伪Leja序列和多维Leja序列，并证明其可用于计算紧集的超限直径、与多复变量Green函数相关，且交织运算保持该性质。

超限直径及其合成

Transfinite diameter and the resultant

本文证明了C^N中集合E通过正则多项式映射F拉回的Fekete-Leja超限直径的一个公式，并将其表示为F的前导部分与E的超限直径的结式.我们还建立了这个公式的nonarchimedean模拟。证明中的一个关键步骤是F的充满朱利亚集的超限直径的公式。