The best m-term trigonometric approximations of the classes of periodic functions of one and many variables in the space B_q,1

2024/10/27 by Kateryna Pozharska, Pozharska, Kateryna, A. S. Romanyuk +1
Mathematics · #Mathematical Approximation and Integration #Mathematical functions and polynomials #Approximation Theory and Sequence Spaces

paper · pdf · doi:10.48550/arxiv.2410.20453

Abstract

Exact order estimates are obtained of the best m-term trigonometric approximations of the Nikol'skii-Besov classes B^r_{p, θ} of periodic functions of one and many variables in the space B_q,1. In the univariate case (d=1), we get the orders of the respective approximation characteristics on the classes B^r_{p, θ} as well as on the Sobolev classes W^r_p, \boldsymbolα in the space B_∞,1 in the case 1≤ p ≤ ∞.

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