We obtain exact lower bounds for Kolmogorov $n$-widths in spaces $C$ and $L$ of classes of convolutions with Neumann kernel $N_{ q,\beta}(t)=\sum\limits_{ k=1}^{ \infty}\dfrac{ q^k}{ k}\cos\left(kt-\dfrac{ \beta\pi}{ 2}\right)$, ${ q\in(0,1)}$, ${ \beta\in\mathbb{ R}}$, for all natural $n$ greater some number which depend only on $q$. The obtained estimates coincide with the best uniform approximations by trigonometric polynomials of mentioned classes. It made possible to obtain exact values for widths of these classes.
Categories: math.CA