Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article Citation - WoS: 1Citation - Scopus: 1Optimal Recovery and Volume Estimates(Academic Press inc Elsevier Science, 2023) Kushpel, AlexanderWe study volumes of sections of convex origin-symmetric bodies in Rn induced by orthonormal systems on probability spaces. The approach is based on volume estimates of John-Lowner ellipsoids and expectations of norms induced by the respective systems. The estimates obtained allow us to establish lower bounds for the radii of sections which gives lower bounds for Gelfand widths (or linear cowidths). As an application we offer a new method of evaluation of Gelfand and Kolmogorov widths of multiplier operators. In particular, we establish sharp orders of widths of standard Sobolev classes Wp & gamma;, & gamma; > 0 in Lq on two-point homogeneous spaces in the difficult case, i.e. if 1 < q < p < oo.& COPY; 2023 Elsevier Inc. All rights reserved.Article Citation - WoS: 3Citation - Scopus: 3The Lebesgue Constants on Projective Spaces(Tubitak, 2021) Kushpel, AlexanderWe 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].Article Citation - WoS: 3Citation - Scopus: 3Lower Bounds of Cowidths and Widths of Multiplier Operators(Academic Press inc Elsevier Science, 2022) Kushpel, AlexanderThe main objective of this article is to present new results on optimal reconstruction of function classes on probability spaces (Omega, A, nu) in the standard L-q spaces. We consider the problem of optimal reconstruction in the sense of the respective cowidths of standard function classes Lambda U-p generated by multiplier or pseudo differential operators Lambda : L-p -> L-q, 1 <= p, q <= infinity. Our approach is based on the estimates of volumes of John-Lowner ellipsoids and expectations of norms induced by orthonormal systems on (Omega, A, nu). It is shown that the results obtained are order sharp in many cases. In particular, we obtain sharp orders of entropy of Sobolev classes W-infinity(gamma), gamma > 0 in L-1 and n-widths of Lambda U-p in L-q, 1 < q <= p < infinity in the case of two-point homogeneous spaces and torus. (C) 2021 Elsevier Inc. All rights reserved.