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

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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 } *.*

## Keywords

Analytic Function Unit Ball Function Class Trigonometric Polynomial Ukrainian National Academy## Preview

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