| Autor: |
Bialas-Ciez, Leokadia, Klimek, Maciej |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
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 {\L}ojasiewicz 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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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