Geodesic
Lower estimates of the widths of the classes of functions defined by a modulus of continuity
Izvestiya. Mathematics , Tome 45 (1995) no. 2, pp. 399-415

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For kernels $K$ satisfying the condition $B_{2m}$ introduced by the author, lower bounds are found for the Kolmogorov widths of classes of convolutions $K\ast H^\omega$, $\omega$ convex, in the uniform metric. In a number of cases these bounds are sharp. 
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     author = {V. T. Shevaldin},
     title = {Lower estimates of the widths of the classes of functions defined by a modulus of continuity},
     journal = {Izvestiya. Mathematics },
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     number = {2},
     year = {1995},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1995_45_2_a7/}
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V. T. Shevaldin. Lower estimates of the widths of the classes of functions defined by a modulus of continuity. Izvestiya. Mathematics , Tome 45 (1995) no. 2, pp. 399-415. http://geodesic.mathdoc.fr/item/IM2_1995_45_2_a7/