Exact Values of Kolmogorov Widths for the Classes of Analytic Functions. II

It is shown that the lower bounds of the Kolmogorov widths d _2n in the space C established in the first part of our work for the function classes that can be represented in the form of convolutions of the kernels ${H}_{h,\beta }(t)={\displaystyle \sum_{k=1}^{\infty}\frac{1}{ \cosh kh} \cos \left(kt-\frac{\beta \pi }{2}\right),\kern1em h>0,\kern1em \beta \in \mathbb{R},}$ with functions φ ⊥ 1 from the unit ball in the space L _∞ coincide (for all n ≥ nh) with the best uniform approximations of these classes by trigonometric polynomials whose order does not exceed n − 1. As a result, we obtain the exact values of widths for the indicated classes of convolutions. Moreover, for all n ≥ nh, we determine the exact values of the Kolmogorov widths d _2n−1 in the space L ₁ of classes of the convolutions of functions φ ⊥ 1 from the unit ball in the space L ₁ with the kernel H _h,β .