Geodesic
Approximation by local trigonometric splines
Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 354-363.

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For the class $W_\infty^{\mathscr L_2}=\{f:f'\in AC,\ \|f''+\alpha^2f\|_\infty\leqslant1\}$ of 1-periodic functions, we use the linear noninterpolating method of trigonometric spline approximation possessing extremal and smoothing properties and locally inheriting the monotonicity of the initial data, i.e., the values of a function from $W_\infty^{\mathscr L_2}$ at the points of a uniform grid. The approximation error is calculated exactly for this class of functions in the uniform metric. It coincides with the Kolmogorov and Konovalov widths. 
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K. V. Kostousov; V. T. Shevaldin. Approximation by local trigonometric splines. Matematičeskie zametki, Tome 77 (2005) no. 3, pp. 354-363. http://geodesic.mathdoc.fr/item/MZM_2005_77_3_a3/

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