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Kolmogorov widths of the intersection of two finite-dimensional balls. (English. Russian original) Zbl 1479.41018

Russ. Math. 65, No. 7, 17-23 (2021); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2021, No. 7, 23-29 (2021).
For \(1\leq p \leq \infty\), let \(B_p^N\) denote the unit ball of the space \(l_p^N\). In the paper, the author obtains order estimates for the Kolmogorov widths \(d_n(B^N_{p_0}\cap \nu B^N_{p_1}; l_q^n)\), where \(1\leq p_1<p_0\leq \infty\), \(n\leq N/2\), \(\nu = k^{1/p_1 - 1/p_0}\), \(k=1,\dots, N\), and \(q<\infty\); in the case of \(q=\infty\), the estimates are obtained only for \(p_1 \geq 2\).

MSC:

41A45 Approximation by arbitrary linear expressions
46B45 Banach sequence spaces
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