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Article overview
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Lower bounds for Kolmogorov widths of classes of Poisson integrals | A. S. Serdyuk
; V. V. Bodenchuk
; | Date: |
2 Apr 2013 | Abstract: | We expand the range of permissible values of $n$ ($ninmathbb{N}$) for which
an arbitrary Poisson kernel
$P_{q,eta}(t)=sumlimits_{k=1}^{infty}q^kcosleft(kt-dfrac{etapi}{2}
ight)$,
${qin(0,1)}$, $etainmathbb{R}$, satisfies Kushpel’s condition $C_{y,2n}$.
As a consequence, we obtain exact values for Kolmogorov widths in the space $C$
($L$) of classes $C_{eta,infty}^q$ ($C_{eta,1}^q$) of Poisson integrals
generated by kernels $P_{q,eta}(t)$ 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. | Source: | arXiv, 1304.0650 | Services: | Forum | Review | PDF | Favorites |
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