On one inequality of different metrics for trigonometric polynomials

Vitalii V. Arestov   ; Marina V. Deikalova

Ural mathematical journal, Tome 8 (2022) no. 2, pp. 27-45

Résumé

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.

Détail

Keywords: trigonometric cosine polynomial in odd harmonics, Nikol'skii different metrics inequality.

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