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

2017/03/14 by В. Ф. Бабенко, Babenko, Vladyslav, Svitlana Konareva +1
Mathematics · #41A #47A #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.1703.04655

openalex publication_date 2017/03/14 · 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\nHilbert space - generalized moduli of continuity\n\ω_\φ(x;L_p,V([0,\δ])) and obtain new exact inequalities of\nJackson - Stechkin type with these moduli of continuity for the approximation\nof elements of a Hilbert space. These results include many well-known\ninequalities for approximation of periodic functions by trigonometric\npolynomials, approximation of non-periodic functions by entire functions of\nexponential type, similar results for almost periodic functions, and others. A\nnumber of results is new even in these classic situations.\n

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