Mean-square approximation by an angle in $L_2$ and the values of quasiwidths for some classes of functions
UDC 517.5 In the metric $L_{2},$ we obtain exact inequalities that associate the best approximations by trigonometrical ``angles'' for functions $f(x,y),$ which are differentiable and $2\pi$-periodic in each variable, with the integrals containing modules of continuity of higher or...
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| Date: | 2020 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2020
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1064 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
In the metric $L_{2},$ we obtain exact inequalities that associate the best approximations by trigonometrical ``angles'' for functions $f(x,y),$ which are differentiable and $2\pi$-periodic in each variable, with the integrals containing modules of continuity of higher order for mixed derivatives of these functions.  For some classes of functions defined by modules of continuity, we calculate Kolmogorov's quasiwidths and linear quasiwidths. |
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| DOI: | 10.37863/umzh.v72i6.1064 |