Geodesic
Relationships between the best uniform polynomial approximations of functions and their even and odd prolongations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 47-52.

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In this paper, we study the relationships between the best uniform polynomial approximations of a continuous function on an interval and its even and odd prolongations. We consider examples that demonstrate the accuracy of the results obtained. Similar issues are also discussed for rational approximations.
Keywords: best uniform polynomial approximation, best uniform rational approximation, even continuation of a function, odd continuation of a function, Jackson's inequality. 
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T. S. Mardvilko. Relationships between the best uniform polynomial approximations of functions and their even and odd prolongations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international winter mathematical school "Modern methods of function theory and related problems", Voronezh, January 27 - February 1, 2023, Part 3, Tome 229 (2023), pp. 47-52. http://geodesic.mathdoc.fr/item/INTO_2023_229_a5/

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