Exact values of Kolmogorov widths of classes of Poisson integrals

A. S. Serdyuk, V. V. Bodenchuk

We prove that the Poisson kernel $P_{q,\beta }(t)=\sum _{k=1}^{\infty }{q}^k\cos (kt-\frac{\beta \pi }{2})$, $q\in (0,1)$, $\beta \in \mathbb{R}$, satisfies Kushpel's condition $C_{y,2n}$ beginni…