Search Results

Now showing 1 - 2 of 2

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 - WoS: 3
Citation - Scopus: 3
The Lebesgue Constants on Projective Spaces
(Tubitak, 2021) Kushpel, Alexander
We give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgueconstants or norms of the Fourier-Laplace projections on the real projective spaces Pd(R). In particular, these resultsextend sharp asymptotic found by Fejer [2] in the case of S1in 1910 and by Gronwall [4] in 1914 in the case of S2. Thecase of spheres, Sd, complex and quaternionic projective spaces, Pd(C), Pd(H) and the Cayley elliptic plane P16(Cay)was considered by Kushpel [8].

Scopus İndeksli Yayınlar Koleksiyonu