Lower bounds for Kolmogorov widths of classes of convolutions with Neumann kernel
Abstract
We obtain exact lower bounds for Kolmogorov $n$-widths in spaces $C$ and $L$ of classes of convolutions with Neumann kernel $N_{q,\beta}(t)=\sum\limits_{k=1}^{\infty}\dfrac{q^k}{k}\cos\left(kt-\dfrac{\beta\pi}{2}\right)$, ${q\in(0,1)}$, ${\beta\in\mathbb{R}}$, 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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2013
- DOI:
- 10.48550/arXiv.1312.6175
- arXiv:
- arXiv:1312.6175
- Bibcode:
- 2013arXiv1312.6175B
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- 41A46
- E-Print:
- 21 pages, in Ukrainian