Poisson积分类Kolmogorov宽度的下界
Lower bounds for Kolmogorov widths of classes of Poisson integrals
摘要：
我们扩大了Poisson核$P_{q,β}(t)=\sum\limits_{k=1}^{\infty}q^k\cos\left(kt-\dfrac{βπ}{2}\right)$、${q\in(0,1)}$、$β\in\mathbb{R}$满足Kushpel条件$C_{y,2n}$的$n$（$n\in\mathbb{N}$）的允许值范围.因此，我们得到精确的值Kolmogorov宽度在空间$C$（$L$）的类$C_{β,\infty}^q$（$C_{β,1}^q$）的泊松积分产生的内核$P_{q,β}(t)$在新的情况下。本文指出，用A.平卡斯
英文摘要：
We expand the ranges of permissible values of $n$ ($n\in\mathbb{N}$) for which Poisson kernels $P_{q,β}(t)=\sum\limits_{k=1}^{\infty}q^k\cos\left(kt-\dfrac{βπ}{2}\right)$, ${q\in(0,1)}$, $β\in\mathbb{R}$, satisfy Kushpel's condition $C_{y,2n}$. As a consequence, we obtain exact values for Kolmogorov widths in the space $C$ ($L$) of classes $C_{β,\infty}^q$ ($C_{β,1}^q$) of Poisson integrals generated by kernels $P_{q,β}(t)$ in new situations. It is shown that obtained here results we can't obtain by using methods of finding of exact lower bounds for widths suggested by A. Pinkus.
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