Work

Estimates of the characteristics of nonlinear approximation of classes of periodic functions of many variables

Year: 2025

Type: article

Abstract: In the paper, we obtained exact order estimates of the best $m$-term trigonometric approximation and the best orthogonal trigonometric approximation of functions from the Nikol'skii-Besov $B^{\boldsymbol{r}}_{p,\theta}(\mathbb{T}^d)$ and Sobolev $W^{\boldsymbol{r}}_{p,\boldsymbol{\alpha}}(\mathbb{T}^d)$ classes in the Lebesque subspaces $B_{q,1}(\mathbb{T}^d)$ for some relations between the parameters $p$ and $q$. The received results yield that estimates of the considered approximation characteristics in the multivariate case, in contrast to the univariate, in the spaces $B_{q,1}(\mathbb{T}^d)$ and $L_q(\mathbb{T}^d)$ differ in order. Besides, for some parameter values the obtained exact order estimates of the best $m$-term trigonometric approximation and the best orthogonal trigonometric approximation in the spaces $B_{q,1}(\mathbb{T}^d)$ still remain unknown for the $L_q(\mathbb{T}^d)$-space.

Source: Carpathian Mathematical Publications

DOI: 10.15330/cmp.17.2.447-460

Authors: K.V. Pozharska, A.S. Romanyuk, S.Ya. Yanchenko

Institutions: National Academy of Sciences of Ukraine, Institute of Mathematics, Chemnitz University of Technology

Language: English

Topic: Mathematical Approximation and Integration

Subfield: Numerical Analysis

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: Science Foundation Ireland, Deutsche Forschungsgemeinschaft

Award: G1840262913