Abstract
We find exact values of upper bounds for the best approximations of q-ellipsoids by polynomials of degree n in the spaces \(S_\phi ^p \) in the case where the approximating polynomials are constructed on the basis of n-dimensional subsystems chosen successively from a given orthonormal system ϕ.
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REFERENCES
A. I. Stepanets, Methods of Approximation Theory [in Russian], Vol. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2002).
A. I. Stepanets, “Approximation characteristics of the spaces S p ? ,” [in Russian], Preprint No. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2001).
A.I. Stepanets, “Approximation characteristics of the spaces S p ? in different metrics,” Ukr. Mat. Zh., 53 No. 8 1121–1146 (2001).
A.I. Stepanets, Approxiamtion Characteristics of the Spaces S p [in Russian], Preprint No. 2, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (2001).
A. I. Stepanets and A. S. Serdyuk, “Direct and inverse theorems on the approximation of functions in the space S p,” Ukr. Mat. Zh., 54, No. 1, 106–124 (2002).
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Stepanets, A.I., Rukasov, V.I. Best “Continuous” n-Term Approximations in the Spaces \(S_\phi ^p \) . Ukrainian Mathematical Journal 55, 801–811 (2003). https://doi.org/10.1023/B:UKMA.0000010257.54302.4a
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DOI: https://doi.org/10.1023/B:UKMA.0000010257.54302.4a