Lower bounds for Kolmogorov widths of classes of convolutions with Neumann kernel

V. V. Bodenchuk

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arXiv · 1312.6175

Lower bounds for Kolmogorov widths of classes of convolutions with Neumann kernel

V. V. Bodenchuk

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Abstract

We obtain exact lower bounds for Kolmogorov $n$-widths in spaces $C$ and $L$ of classes of convolutions with Neumann kernel $N_{q,β}(t)=\sum\limits_{k=1}^{\infty}\dfrac{q^k}{k}\cos\left(kt-\dfrac{βπ}{2}\right)$, ${q\in(0,1)}$, ${β\in\mathbb{R}}$, 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.

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BibTeX RIS

V. V. Bodenchuk. 2013-12-20. Lower bounds for Kolmogorov widths of classes of convolutions with Neumann kernel. https://arxiv.org/abs/1312.6175

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