We obtain exact order estimates for the best M-term trigonometric approximations of the Besov classes B ∞,θ r in the space L q . We also determine the exact orders of the best bilinear approximations of the classes of functions of 2d variables generated by functions of d variables from the classes B p,θ r with the use of translation of arguments.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 4, pp. 536–551, April, 2010.
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Romanyuk, A.S., Romanyuk, V.S. Asymptotic estimates for the best trigonometric and bilinear approximations of classes of functions of several variables. Ukr Math J 62, 612–629 (2010). https://doi.org/10.1007/s11253-010-0375-x
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DOI: https://doi.org/10.1007/s11253-010-0375-x