Müntz spaces and Remez inequalities

Weighted Remez- and Nikolskii-Type Inequalities on a Quasismooth Curve

We establish sharp $L_p,1\le p<\infty$ weighted Remez- and Nikolskii-type inequalities for algebraic polynomials considered on a quasismooth (in the sense of Lavrentiev) curve in the complex plane.

超球面多项式三角多项式的Remez型不等式

Remez-type inequalities for the hyperbolic cross polynomials

本文研究了具有超球面谐波的三角多项式的Remez型不等式，探讨了Remez与Nikolskii不等式之间的关系及其应用。

Smooth rigidity and Remez-type inequalities

If a smooth function of one variable has maximum one on the unit interval, and has there $d$ zeroes, then its $(d+1)$-st derivative must be "big". This is one of the simplest examples of what we call "smooth rigidity": certain geometric properties of zero sets of smooth functions $f$ imply explicit lower bounds on the high-order derivatives of $f$. In dimensions greater than one, the powerful one-dimension tools, like Lagrange's remainder formula, and divided finite differences, are not directly applicable. Still, the result above implies, via line sections, rather strong restrictions on zeroe…

驯服集上的有效拟解析Remez不等式

Effective quasianalytic Remez inequalities on tame sets

针对拟解析Denjoy-Carleman类函数，在具有驯服几何的大类胖紧集上建立了Remez不等式，推广了经典多项式Remez不等式，并导出了子水平集体积估计、L^p范数比较、Lojasiewicz、Harnack和Markov型不等式等定量结果。

Smooth rigidity and Remez inequalities via Topology of level sets

A smooth rigidity inequalitiy provides an explicit lower bound for the $(d+1)$-st derivatives of a smooth function $f$, which holds, if $f$ exhibits certain patterns, forbidden for polynomials of degree $d$. The main goal of the present paper is twofold: first, we provide an overview of some recent results and questions related to smooth rigidity, which recently were obtained in Singularity Theory, in Approximation Theory, and in Whitney smooth extensions. Second, we prove some new results, specifically, a new Remez-type inequality, and on this base we obtain a new rigidity inequality. In both…

关于一种用计算机证明不等式的方法的注记

Some notes on a method for proving inequalities by computer

本文基于Remez算法，探讨了一种用计算机证明不等式的方法的数学基础，指出该方法在实践中通常成为验证不等式的启发式方法，并改进了现有定理中基于数值验证的不等式。