Estimations of the best M-term approximations of functions in the Lorentz space with constructive methods

Gabdolla Akishevich Akishev

2017

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DOI 10.31489/2017m3/13-26

Data confidence 70 medium

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Abstract

Estimations of the best M -term approximations of functions in the Lorentz space with constructive methodsThis paper considers the Lorentz space of periodic functions of many variables with the anisotropic norm, of functional Nikol'skii-Besov's class and of the best M -term approximation of function.We have established sufficient conditions for the function to belong to one of the Lorentz spaces in another.We obtain upper and lower bounds for the best M -member approximations of functions from the Nikol'skii-Besov class in the anisotropic Lorentz space To prove the upper bound, we used a new constructive method developed by V.N.Temlyakov.