Best m-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes of periodic functions of several variables

Authors

https://doi.org/10.15330/cmp.17.1.67-81

Keywords:

periodic function of several variables, Nikol'skii-Besov-type class, best m-term trigonometric approximation
Published online: 2025-04-21

Abstract

We obtained the exact order estimates of the best m-term trigonometric approximations of the isotropic Nikol'skii-Besov-type classes Bωp,θ of periodic functions of several variables in the spaces Bq,1 for 1<p<q<, q2. A peculiarity of these spaces, as linear subspaces of Lq, is that the norm in them is stronger than the Lq-norm. It was found that the obtained estimates of the considered approximation characteristic coincide in order with the estimates of the corresponding characteristic of the classes Bωp,θ in the spaces Lq.

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Fedunyk-Yaremchuk, O.; Hembars'ka, S.; Romanyuk, I. Best m-Term Trigonometric Approximations of the Isotropic Nikol’skii-Besov-Type Classes of Periodic Functions of Several Variables. Carpathian Math. Publ. 2025, 17, 67-81.

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