Estimates of characteristics of nonlinear approximation of classes of periodic functions
In the paper we make an overview of results concerning order estimates of the best m-term (sparse) trigonometric approximation and the best orthogonal trigonometric approximation of the Stepanets classes of multi- and univariate functions with bounded generalized derivatives in the Lebesque space. I...
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| Date: | 2025 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2025
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/545 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | In the paper we make an overview of results concerning order estimates of the best m-term (sparse) trigonometric approximation and the best orthogonal trigonometric approximation of the Stepanets classes of multi- and univariate functions with bounded generalized derivatives in the Lebesque space. In addition, we formulate exact-order estimates for these approximation characteristics for the isotropic Nikol'skii-Besov classes with bounded differences in a certain Lebesque subspace. In particular, the case of small smoothness is considered of functions from the respective classes. |
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| DOI: | 10.3842/trim.v21n1.545 |