The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$

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 $B_{\infty,1}$ in the case $1\leq p \leq \infty$.

Theorems & Definitions (11)

• Theorem 2.1
• proof : Proof of Theorem \ref{['Th 1']}
• Theorem 2.2
• proof : Proof of Theorem \ref{['Thm2']}
• Remark 2.3
• Theorem 3.1
• proof : Proof of Theorem \ref{['Thm3']}
• Remark 3.2
• Theorem 3.3
• proof : Proof of Theorem \ref{['Thm4']}