论文标题
在代数集上的ogojasiewicz指数和pluricomplex绿色功能
Łojasiewicz exponent and pluricomplex Green function on algebraic sets
论文作者
论文摘要
我们研究了代数集的多重果实绿色功能。令$ f $为两个代数套件之间的合适的霍明型映射。鉴于$ f $的紧凑型套装$ k $，我们展示了如何估计$ k $的pluricomplex绿色功能和$ f^{ - 1}（k）$的$ f $ f $ $ f $和$ f $的增长指数。该结果导致了代数集上的多膜绿色功能的明确例子。我们还提出了伯恩斯坦 - 瓦尔斯（Bernstein-Walsh）多项式不平等的增强版本。本文提供了一个理论框架，用于未来研究伯恩斯坦 - 瓦尔斯·西西亚克定理风格的全态函数多项式近似速率。
We study pluricomplex Green functions on algebraic sets. Let $f$ be a proper holomorphic mapping between two algebraic sets. Given a compact set $K$ in the range of $f$, we show how to estimate the pluricomplex Green functions of $K$ and of $f^{-1}(K)$ in terms of each other, the Łojasiewicz exponent of $f$ and the growth exponent of $f$. This result leads to explicit examples of pluricomplex Green functions on algebraic sets. We also present an enhanced version of the Bernstein-Walsh polynomial inequality specific to algebraic sets. This article provides a theoretical framework for future investigations of the rate of polynomial approximation of holomorphic functions on algebraic sets in the style of Bernstein-Walsh-Siciak theorem.
