Browsing by Author "Kushpel, A. K."

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Citation - WoS: 3
Citation - Scopus: 3
Estimates of Entropy for Multiplier Operators of Systems of Orthonormal Functions
(Academic Press inc Elsevier Science, 2023) Milare, J.; Kushpel, A. K.; Tozoni, S. A.
We obtain upper and lower estimates for epsilon-entropy and entropy numbers of multiplier operators of systems of orthonormal functions bounded from Lp to Lq. Upper estimates in our study require that a Marcinkiewicz-type multiplier theorem is available for the system. As application we obtain estimates for epsilon-entropy and entropy numbers of the multiplier operators associated with the sequences (k-gamma (lnk)-xi)infinity k=2 and (e-gamma kr )infinity k=0 where gamma > 0, xi >= 0 and 0 < r < 1. Some of these estimates are order sharp. We verify that the trigonometric system on the circle, the Vilenkin system and the Walsh system satisfy the conditions of our study. We also study analogous results for the Haar system and the Walsh systems on spheres.(c) 2022 Elsevier Inc. All rights reserved.
John-Lowner Ellipsoids and Entropy of Multiplier Operators on Rank 1 Compact Homogeneous Manifolds
(Steklov Mathematical inst, Russian Acad Sciences, 2025) Kushpel, A. K.
We present a new method of the evaluation of entropy, which is based on volume estimates for John-Lowner ellipsoids induced by the eigenfunctions of Laplace-Beltrami operator on compact homogeneous manifolds M-d of rank 1. This approach gives the sharp orders of entropy in the situations where the known methods meet difficulties of fundamental nature. In particular, we calculate the sharp orders of the entropy of the Sobolev classes W-p(gamma) (M-d), gamma> 0, in L-q(M-d), 1 <= q <= p <= infinity. Bibliography: 35 titles.
Citation - WoS: 3
Citation - Scopus: 2
On the Lebesgue Constants
(Springer, 2020) Kushpel, A. K.
We present the solution of a classical problem of approximation theory about the sharp asymptotics of Lebesgue constants or the norms of Fourier-Laplace projections on the real sphere S-d, in complex P-d (C) and quaternionic P-d(H) projective spaces, and in the Cayley elliptic plane P-16(Cay). In particular, these results supplement the sharp asymptotics established by Fejer (1910) in the case of S-1 and by Gronwall (1914) in the case of S-2.