关于三角多项式的一个不同度量不等式

Q3 Mathematics Ural Mathematical Journal Pub Date : 2022-12-29 DOI:10.15826/umj.2022.2.003

V. Arestov, M. Deikalova

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引用次数: 0

摘要

我们研究了具有奇次谐波的余弦系统（\mathscr｛C｝＝cos（2k+1）x｝_｛k＝0｝^infty）中多项式的一致范数与（L^p（0，\pi/2））-范数之间的尖锐不等式。我们研究了该不等式中最佳常数相对于多项式阶数的极限行为，并给出了固定多项式阶数不等式中极值多项式的特征。

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ON ONE INEQUALITY OF DIFFERENT METRICS FOR TRIGONOMETRIC POLYNOMIALS

We study the sharp inequality between the uniform norm and \(L^p(0,\pi/2)\)-norm of polynomials in the system \(\mathscr{C}=\{\cos (2k+1)x\}_{k=0}^\infty\) of cosines with odd harmonics. We investigate the limit behavior of the best constant in this inequality with respect to the order \(n\) of polynomials as \(n\to\infty\) and provide a characterization of the extremal polynomial in the inequality for a fixed order of polynomials.

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