Geodesic
On the precise values of $n$-widths for classes defined by cyclic variation diminishing operators
Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1371-1383

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A general approach to the problems of precise calculation of $n$-widths in the uniform metric is proposed for the classes of 2$\pi$-periodic functions defined by (not necessarily linear) operators having certain oscillation properties. This approach enables one to obtain precise results on $n$-widths both for classes of functions representable as convolutions with cyclic variation diminishing kernels and for some classes of analytic functions not representable as such convolutions. 
@article{SM_1997_188_9_a5,
     author = {K. Yu. Osipenko},
     title = {On the precise values of $n$-widths for classes defined by cyclic variation diminishing operators},
     journal = {Sbornik. Mathematics},
     pages = {1371--1383},
     publisher = {mathdoc},
     volume = {188},
     number = {9},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_9_a5/}
}
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K. Yu. Osipenko. On the precise values of $n$-widths for classes defined by cyclic variation diminishing operators. Sbornik. Mathematics, Tome 188 (1997) no. 9, pp. 1371-1383. http://geodesic.mathdoc.fr/item/SM_1997_188_9_a5/