Geodesic
Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation
Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 43-52

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The $(2n-1)$-dimensional diameter of the class $W^rL$ is found in the metric of the space $L(0,2\pi)$. The rate of convergence is also studied of the interpolating spline functions $S_r(x,h)$ with equidistant nodes to a function $F(x)$ which has a uniformly continuous $k$-th derivative $(r\ge k\ge0)$ on the entire axis. 
@article{MZM_1970_7_1_a4,
     author = {Yu. N. Subbotin},
     title = {Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {43--52},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {1970},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a4/}
}
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Yu. N. Subbotin. Diameter of class $W^rL$ in $L(0,2\pi)$ and spline function approximation. Matematičeskie zametki, Tome 7 (1970) no. 1, pp. 43-52. http://geodesic.mathdoc.fr/item/MZM_1970_7_1_a4/