Estimates from below for Kolmogorov widths in classes of Poisson integral
We expand the ranges of permissible values of $n$ ($n\in\mathbb{N}$) for which Poisson kernels $P_{q,\beta}(t)=\sum\limits_{k=1}^{\infty}q^k\cos\left(kt-\dfrac{\beta\pi}{2}\right)$, ${q\in(0,1)}$, $\beta\in\mathbb{R}$, satisfy Kushpel's condition $C_{y,2n}$. As a consequence, we obtain exac...
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| Date: | 2013 |
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| Keywords: | keywords |
| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
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Інститут математики НАН України
2013
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/170 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | We expand the ranges of permissible values of $n$ ($n\in\mathbb{N}$) for which Poisson kernels $P_{q,\beta}(t)=\sum\limits_{k=1}^{\infty}q^k\cos\left(kt-\dfrac{\beta\pi}{2}\right)$, ${q\in(0,1)}$, $\beta\in\mathbb{R}$, satisfy Kushpel's condition $C_{y,2n}$. As a consequence, we obtain exact values for Kolmogorov widths in the space $C$~($L$) of classes $C_{\beta,\infty}^q$~($C_{\beta,1}^q$) of Poisson integrals generated by kernels $P_{q,\beta}(t)$ 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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