We give an exposition of some simple but applicable cases of worst-case growth of a polynomial in terms of its uniform norm on a given compact set K ⊂ ℂ d . Included is a direct verification of the formula for the pluripotential extremal function for a real simplex. Throughout we attempt to make the exposition as accessible to a general (analytic) audience as possible, avoiding wherever possible the finer details of Pluripotential Theory.

中文翻译：

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多项式的极值增长

我们根据多项式在给定紧集 K ⊂ ℂ d 上的统一范数给出了多项式最坏情况增长的一些简单但适用的情况。其中包括对真实单纯形的多势极值函数公式的直接验证。在整个过程中，我们试图让一般（分析）观众尽可能容易理解这一论述，尽可能避免多能理论的更精细细节。