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Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Browsing Matematik Bölümü Yayın Koleksiyonu by Institution Author "Kushpel, Alexander"

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    Citation - WoS: 3
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    Lower Bounds of Cowidths and Widths of Multiplier Operators
    (Academic Press inc Elsevier Science, 2022) Kushpel, Alexander
    The 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.
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    Citation - WoS: 1
    Citation - Scopus: 1
    Optimal Recovery and Volume Estimates
    (Academic Press inc Elsevier Science, 2023) Kushpel, Alexander
    We 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.