On the best polynomial approximation of $$$2\pi$$$-periodic functions in the $$$L_2$$$ space

S.B. Vakarchuk

doi:10.15421/241503

On the best polynomial approximation of $$$2\pi$$$-periodic functions in the $$$L_2$$$ space

S.B. Vakarchuk (Alfred Nobel Dnipropetrovsk university), https://orcid.org/0000-0002-2562-8844

Abstract

On the classes $$$L^r_2$$$, where $$$r\in {\mathbb{Z}}_+$$$, exact constants of Jackson type inequalities have been obtained for the characteristics of smoothness $$${\Delta}_k (f)$$$, $$$k\in \mathbb{N}$$$, which are defined by the averaged $$$k$$$-th order finite differences of functions $$$f\in L_2$$$.

Keywords

best polynomial approximation; k-th order finite difference; partial sum of Fourier series

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References

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