Let $V\subset {\mathbb{R}}^m$ be a centrally symmetric convex body and let $V^{\ast }\subset {\mathbb{R}}^m$ be its polar. We prove limit relations between the sharp constants in the multivariate Markov–Bernstein–Nikolskii type inequalities for algebraic polynomials on $V^{\ast }$ and the corresponding constants for entire functions of exponential type with the spectrum in $V$.

中文翻译：

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近似理论的尖锐常数。三，凸集上不同度量的某些多项式不等式

让 $V\subset {\mathbb{[R}}^{米}$ 是一个中心对称的凸体，让 $V^{\ast }\subset {\mathbb{[R}}^{米}$是它的极地。我们证明了代数多项式的多元Markov-Bernstein-Nikolskii型不等式中的尖锐常数之间的极限关系$V^{\ast }$ 以及频谱为的指数型整个函数的相应常数 $V$。