On the precise values of $n$-widths for classes defined by cyclic variation diminishing operators

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.