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Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds
(Tubitak, 2021) LEVESLEY, Jeremy; KUSHPEL, Alexander; Taş, Kenan
We develop a general method to calculate entropy and n-widths of sets of smooth functions on an arbitrary compact homogeneous Riemannian manifold Md . Our method is essentially based on a detailed study of geometric characteristics of norms induced by subspaces of harmonics on Md . This approach has been developed in the cycle of works [1, 2, 10–19]. The method’s possibilities are not confined to the statements proved but can be applied in studying more general problems. As an application, we establish sharp orders of entropy and n-widths of Sobolev’s classes Wγ p ( Md ) and their generalisations in Lq ( Md ) for any 1 < p, q < ∞. In the case p, q = 1, ∞ sharp in the power scale estimates are presented.
Citation - Scopus: 1
On The Problem Of Schoenberg On Rn
(University of Prishtina, 2024) Kushpel, Alexander; Taş, Kenan

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