Geodesic
Approximation of certain classes of differentiable periodic functions by interpolational splines in a~uniform decomposition
Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 955-966.

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In this paper we obtain upper and lower bounds of a uniform approximation by interpolational splines of order $r$ in a uniform decomposition on the classes of functions $W^rH_\omega$ and $W_L^{r+2}$ and on the whole space $C^r$. 
@article{MZM_1974_15_6_a14,
     author = {A. A. Zhensykbaev},
     title = {Approximation of certain classes of differentiable periodic functions by interpolational splines in a~uniform decomposition},
     journal = {Matemati\v{c}eskie zametki},
     pages = {955--966},
     publisher = {mathdoc},
     volume = {15},
     number = {6},
     year = {1974},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a14/}
}
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A. A. Zhensykbaev. Approximation of certain classes of differentiable periodic functions by interpolational splines in a~uniform decomposition. Matematičeskie zametki, Tome 15 (1974) no. 6, pp. 955-966. http://geodesic.mathdoc.fr/item/MZM_1974_15_6_a14/