Improvement of a Theorem of Lorentz (1963) and its Generalization to the Multivariate Case
Classical Analysis and ODEs
2016-11-30 v2
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.
Keywords
Cite
@article{arxiv.1610.01448,
title = {Improvement of a Theorem of Lorentz (1963) and its Generalization to the Multivariate Case},
author = {Zhong Guan and Tao Wang},
journal= {arXiv preprint arXiv:1610.01448},
year = {2016}
}