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Kolmogorov widths of intersections of finite-dimensional balls. (English) Zbl 1507.41011

Summary: In the present paper, order estimates for the \(n\) th Kolmogorov widths of the intersection of homothetic copies of the unit balls \(\nu_\alpha B_{p_\alpha}^N\) in \(l_q^N\) are obtained for \(n \leqslant N / 2\). This result for \(n = N / 2\) was obtained by Galeev in 1981.

MSC:

41A46 Approximation by arbitrary nonlinear expressions; widths and entropy
46B20 Geometry and structure of normed linear spaces
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