Inequalities of Jackson-Stechkin type for elements of Hilbert space (in Russian)

2017/03/14 by Vladyslav Babenko, В. Ф. Бабенко, Babenko, Vladyslav +2
Mathematics · #41A #47A #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration #math.FA #msc:41A #msc:47A

paper · pdf · doi:10.48550/arxiv.1703.04655

in Russian

arxiv created 2017/03/14 · openalex publication_date 2017/03/14 · arxiv updated 2017/03/16 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this paper we introduced a new characteristics of the elements of a Hilbert space - generalized moduli of continuity ω_φ(x;L_p,V([0,δ])) and obtain new exact inequalities of Jackson - Stechkin type with these moduli of continuity for the approximation of elements of a Hilbert space. These results include many well-known inequalities for approximation of periodic functions by trigonometric polynomials, approximation of non-periodic functions by entire functions of exponential type, similar results for almost periodic functions, and others. A number of results is new even in these classic situations.

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