Levesley, JeremyTas, KenanKushpel, Alexander2022-01-312025-09-182022-01-312025-09-182021Kushpel, Alexander; Taş, Kenan; Levesley, Jeremy (2021). "Widths and entropy of sets of smooth functions on compact homogeneous manifolds", Turkish Journal of Mathematics, Vol. 45, No. 1, pp. 167-184.1300-00981303-6149https://doi.org/10.3906/mat-1911-79https://search.trdizin.gov.tr/en/yayin/detay/531078/widths-and-entropy-of-sets-of-smooth-functions-on-compact-homogeneous-manifoldshttps://hdl.handle.net/20.500.12416/14322We develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary\rcompact homogeneous Riemannian manifold Md\r. Our method is essentially based on a detailed study of geometric\rcharacteristics of norms induced by subspaces of harmonics on Md\r. This approach has been developed in the cycle\rof works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in\rstudying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s\rclasses Wγ\rp\r(\rMd\r)\rand their generalisations in Lq\r(\rMd\r)\rfor any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power\rscale estimates are presented.eninfo:eu-repo/semantics/openAccessMatematikArticle10.3906/mat-1911-792-s2.0-85100624710