Geodesic
On One Generalized Translation and the Corresponding Inequality of Different Metrics
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 40-53

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In this paper, we discuss the properties of the generalized translation operator generated by the system of functions $\left\{ \cos\left(\frac{(2k-1)\pi }{2}t\right)\right\}_{k=1}^\infty$ in the spaces $L^p(0,1)$, $p\ge 1$. The translation operator is applied to the study of the Nikol'skii inequality between the uniform norm and the $L^p$-norm of polynomials in this system.
Keywords: generalized translation operator, trigonometric polynomial, inequality of different metrics. 
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V. V. Arestov; M. V. Deikalova. On One Generalized Translation and the Corresponding Inequality of Different Metrics. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 28 (2022) no. 4, pp. 40-53. http://geodesic.mathdoc.fr/item/TIMM_2022_28_4_a3/