椭圆上代数多项式的不等式

Q3 Mathematics Ural Mathematical Journal Pub Date : 2020-12-26 DOI:10.15826/umj.2020.2.009

Tatiana M. Nikiforova

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引用次数: 0

摘要

本文给出了逼近理论中两个经典问题的新解。第一个问题是找到在椭圆上与零偏差最小的多项式。第二个问题是找出一个实数系数在线段\([- 1,1]\)上归一化的代数多项式的导数在焦点为\(\pm 1\)的椭圆上的一致范数的确切上界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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INEQUALITIES FOR ALGEBRAIC POLYNOMIALS ON AN ELLIPSE

The paper presents new solutions to two classical problems of approximation theory. The first problem is to find the polynomial that deviates least from zero on an ellipse. The second one is to find the exact upper bound of the uniform norm on an ellipse with foci \(\pm 1\) of the derivative of an algebraic polynomial with real coefficients normalized on the segment \([- 1,1]\).

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