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arXiv · 1610.01448

Improvement of a Theorem of Lorentz (1963) and its Generalization to the Multivariate Case

Zhong Guan·Tao Wang
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Abstract

In this short note we have proved an enhanced version of a theorem of Lorentz [1] and its generalization to the multivariate case which gives a non- uniform estimate of degree of approximation by a polynomial with positive coefficients. The performance of the approximation at the vertices of [0; 1]d is more precisely characterized by the improved result and its multivariate generalization. The latter provides mathematical foundation on which multivariate density approximation by a polynomial with positive coefficients can be established.

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Zhong Guan, Tao Wang. 2016-09-27. Improvement of a Theorem of Lorentz (1963) and its Generalization to the Multivariate Case. https://arxiv.org/abs/1610.01448

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