多元Newman不等式与逼近逆定理

Multivariate Newman Inequality and Converse Theorems of Approximation

本文研究多元有理逼近的Newman不等式与逼近逆定理问题.在多元Müntz多项式空间中利用分解方法建立多元有理多项式的Markov型不等式与Nikolskii型不等式.同时,建立多元有理逼近的逆定理,即Steckin型不等式.本文所获结果不仅推广了一元的相应结果,而且包含了关于代数多项式的一些经典结果.

This paper deals with the problems of Newman inequality and converse theorems in multivariate rational approximation.By using a technique of decomposition in Müntz polynomial space,the Markov- and Nikolskii-type inequalities are established.The inverse theorems of rational approximation,which are called Steckin-type inequalities,are also given.The obtained results not only expand the corresponding ones of univariable,but also contain some classical ones of algebraic polynomials.