Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article The Lebesgue Constants on Projective Spaces(Tubitak Scientific & Technological Research Council Turkey, 2021) Kushpel, AlexanderWe give the solution of a classical problem of Approximation Theory on sharp asymptotic of the Lebesgue constants or norms of the Fourier-Laplace projections on the real projective spaces P-d (R). In particular, these results extend sharp asymptotic found by Fejer [2] in the case of S-1 in 1910 and by Gronwall [4] in 1914 in the case of S-2. The case of spheres, S-d, complex and quaternionic projective spaces, P-d(C), P-d(H) and the Cayley elliptic plane P-16 (Cay) was considered by Kushpel [8].Article Citation - WoS: 5Citation - Scopus: 5Widths and Entropy of Sets of Smooth Functions on Compact Homogeneous Manifolds(Tubitak Scientific & Technological Research Council Turkey, 2021) Levesley, Jeremy; Tas, Kenan; Kushpel, AlexanderWe 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.