Approximation of functions of many variables from the generalization Nikol'skii-Besov type classes in the uniform and integral metrics

2024/03/27 by M. Gromyak, Gromyak, M. I., O. Ya. Radchenko +3
Mathematics · #41A30 #41A50 #41A63 #42A38 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2403.18414

openalex publication_date 2024/03/27 · openalex created_date 2024/03/29 · openalex updated_date 2026/07/28

Abstract

We obtain the exact order estimates of the approximation of the functions of many variables from the generalized Nikol'skii-Besov classes B^Ω_p,θ(ℝ^d) by sums of de la Vallee Poussin type in the metrics space L_∞(ℝ^d) and L₁(ℝ^d). These classes of functions for some given Ω coincide with the well-known classical Nikol'skii-Besov isotropic classes.

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