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arXiv · 1901.04458

Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics

Michael I. Ganzburg
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Abstract

We prove invariance theorems for general inequalities of different metrics and apply them to limit relations between the sharp constants in the multivariate Markov-Bernstein-Nikolskii type inequalities with the polyharmonic operator for algebraic polynomials on the unit sphere and the unit ball in $\R^m$ and the corresponding constants for entire functions of spherical type on $\R^m$. Certain relations in the univariate weighted spaces are discussed as well.

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Michael I. Ganzburg. 2019-01-14. Sharp Constants of Approximation Theory. II. Invariance Theorems and Certain Multivariate Inequalities of Different Metrics. https://doi.org/10.1007/s00365-019-09481-2

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