The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913565533798400 |
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| author | Pozharska, Kateryna Romanyuk, Anatolii |
| author_facet | Pozharska, Kateryna Romanyuk, Anatolii |
| contents | 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 $1\leq p \leq \infty$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_20453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$ Pozharska, Kateryna Romanyuk, Anatolii Classical Analysis and ODEs 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 $1\leq p \leq \infty$. |
| title | The best $m$-term trigonometric approximations of the classes of periodic functions of one and many variables in the space $B_{q,1}$ |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2410.20453 |