Metric entropy, \(n\)-widths, and sampling of functions on manifolds (Q1685946)

The authors determine the asymptotics of the Kolmogorov entropy and \(n\)-widths for the suitably defined approximation spaces on manifolds and quasi-metric measure spaces. The corresponding asymptotically optimal algorithms to represent functions within a prescribed accuracy are suggested. Some related results for function on compact smooth manifolds can be found in [\textit{H. N. Mhaskar}, Neural Netw. 24, No. 4, 345--359 (2011; Zbl 1222.42036)] and [\textit{Yu. A. Farkov}, J. Math. Sci., New York 218, No. 5, 678--698 (2016; Zbl 1355.30035); translation from Fundam. Prikl. Mat. 19, No. 5, 185--212 (2014)].