A quantitative estimate for the Trotter’s approximation theorem for the limiting semigroup of operators generated by the multidimensional Bernstein operators on a simplex is obtained. For this, an essential step consists in an explicit representation of the derivatives of higher order of multidimensional Bernstein operators.

中文翻译：

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由多维 Bernstein 算子生成的极限半群的定量结果

获得了由单形上的多维伯恩斯坦算子生成的有限半群算子的 Trotter 逼近定理的定量估计。为此，一个重要的步骤在于明确表示多维伯恩斯坦算子的高阶导数。