Vasil’eva, A. A. 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 \(p_1 \geq 2\). Reviewer: Yuri A. Farkov (Moskva) Cited in 2 Documents MSC: 41A45 Approximation by arbitrary linear expressions 46B45 Banach sequence spaces Keywords:Kolmogorov widths; intersection of finite-dimensional balls PDFBibTeX XMLCite \textit{A. A. Vasil'eva}, Russ. Math. 65, No. 7, 17--23 (2021; Zbl 1479.41018); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2021, No. 7, 23--29 (2021) Full Text: DOI arXiv References: [1] Tikhomirov, V. M., Approximation theory, Analysis-2, 103-260 (1987), Moscow: VINITI AN SSSR, Moscow · Zbl 0655.41002 [2] Pietsch, A., s-numbers of operators in Banach space, Studia Math., 51, 201-223 (1974) · Zbl 0294.47018 [3] Stesin, M. I., Aleksandrov diameters of finite-dimensional sets and classes of smooth functions, Dokl. Akad. Nauk SSSR, 220, 6, 1278-1281 (1975) · Zbl 0333.46012 [4] Kashin, B. S., The diameters of octahedra, Uspekhi Mat. Nauk, 30:4, 184, 251-252 (1975) · Zbl 0311.46014 [5] Kashin, B. S., Diameters of some finite-dimensional sets and classes of smooth functions, Math. USSR-Izv., 11, 2, 317-333 (1977) · Zbl 0378.46027 [6] Gluskin, E. D., On some finite-dimensional problems from the theory of widths,, Vestnik Lenin. Univ., 13, 5-10 (1981) · Zbl 0482.41018 [7] Gluskin, E. D., Norms of random matrices and widths of finite-dimensional sets, Math. USSR-Sb., 48, 1, 173-182 (1984) · Zbl 0558.46013 [8] Garnaev, A. Yu.; Gluskin, E. D., The widths of a Euclidean ball, Dokl. Akad. Nauk SSSR, 277, 5, 1048-1052 (1984) · Zbl 0588.41022 [9] Galeev, E. M., The Kolmogorov diameter of the intersection of classes of periodic functions and of finite-dimensional sets, Math. Notes, 29, 5, 382-388 (1981) · Zbl 0507.41020 [10] Galeev, E. M., Widths of functional classes and finite-dimensional sets, Vladikavk. Math. J., 13, 2, 3-14 (2011) · Zbl 1238.46025 [11] Vasil’eva A.A. “Kolmogorov widths of weighted Sobolev classes on a multi-dimensional domain with conditions on the derivatives of order r and zero”, arXiv:2004.06013. [12] Gluskin, E. D., Intersections of a cube with an octahedron are poorly approximated by low-dimensional subspaces, Approximation of Functions by Special Classes of Operators. Interuniversity collection of scientific papers, 35-41 (1987), Vologda: Min. pros. RSFSR, Vologodsk. gos. ped. inst., Vologda · Zbl 0685.46007 [13] Malykhin, Yu. V.; Ryutin, K. S., The product of octahedra is badly approximated in the \(l_{2,1}\)-metric, Math. Notes, 101, 1, 94-99 (2017) · Zbl 1371.52008 [14] Vasil’eva, A. A., Widths of function classes on sets with tree-like structure, J. Appr. Theory, 192, 19-59 (2015) · Zbl 1312.41035 [15] Konyagin, S. V.; Malykhin, Yu. V.; Ryutin, K. S., On exact recovery of sparse vectors from linear measurements, Math. Notes, 94, 1, 107-114 (2013) · Zbl 1323.15013 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.