English

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

Functional Analysis 2017-03-16 v1

Abstract

In this paper we introduced a new characteristics of the elements of a Hilbert space - generalized moduli of continuity ωφ(x;Lp,V([0,δ]))\omega_\varphi(x;L_{p,V}([0,\delta])) 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.

Keywords

Cite

@article{arxiv.1703.04655,
  title  = {Inequalities of Jackson-Stechkin type for elements of Hilbert space (in Russian)},
  author = {Vladyslav Babenko and Svitlana Konareva},
  journal= {arXiv preprint arXiv:1703.04655},
  year   = {2017}
}

Comments

in Russian