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- W4310926898 abstract "We study volumes of sections of convex origin-symmetric bodies in $mathbb{R}% ^{n}$ induced by orthonormal systems on probability spaces. The approach is based on volume estimates of John-L{o}wner ellipsoids and expectations of norms induced by the respective systems. The estimates obtained allows us to establish lower bounds for the radii of sections which gives lower bounds for Gelfand widths (or linear cowidths). As an application we offer a new method of evaluation of Gelfand and Kolmogorov widths of multiplier operators. In particular, we establish sharp orders of widths of standard Sobolev classes $W_{p}^{gamma }$ in $L_{q}$ in the difficult case, i.e. $% 1<qleq pleq infty $." @default.
- W4310926898 created "2022-12-21" @default.
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- W4310926898 date "2022-12-07" @default.
- W4310926898 modified "2023-10-16" @default.
- W4310926898 title "Volume estimates and their applications in the problem of optimal recovery" @default.
- W4310926898 doi "https://doi.org/10.48550/arxiv.2212.03834" @default.
- W4310926898 hasPublicationYear "2022" @default.
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