Geodesic
Approximation of Periodic Functions Using $\mathrm{mup}_s(x)$
Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 878-901

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The spaces of linear combinations of the shifts of a compactly supported solution of a functional-differential equation are considered. It is proved that they are asymptotically extremal for approximating, in the norm of $L_2$, functions from the classes $\widetilde{W}_2^r$.
Keywords: approximation of periodic functions, the classes $\widetilde{W}_2^r$, functional-differential equation, the function $mup_s(x)$, basis function, Taylor series, linear operator. 
@article{MZM_2013_93_6_a7,
     author = {V. A. Makarichev},
     title = {Approximation of {Periodic} {Functions} {Using} $\mathrm{mup}_s(x)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {878--901},
     publisher = {mathdoc},
     volume = {93},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a7/}
}
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V. A. Makarichev. Approximation of Periodic Functions Using $\mathrm{mup}_s(x)$. Matematičeskie zametki, Tome 93 (2013) no. 6, pp. 878-901. http://geodesic.mathdoc.fr/item/MZM_2013_93_6_a7/