Approximation by Fourier sums in classes of Weyl – Nagy differentiable functions with high exponent of smoothness
UDC 517.5 We establish asymptotic estimates for the least upper bound of approximations in the uniform metric by Fourier sums of order $n-1$ in classes of $2\pi$-periodic Weyl-Nagy differentiable functions $W^r_{\beta,p},$ $1\le p\le \infty,$ $\beta\in\mathbb{R},$ with high exponents of smoothness $...
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| Date: | 2022 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2022
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7136 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
| Download file: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 517.5
We establish asymptotic estimates for the least upper bound of approximations in the uniform metric by Fourier sums of order $n-1$ in classes of $2\pi$-periodic Weyl-Nagy differentiable functions $W^r_{\beta,p},$ $1\le p\le \infty,$ $\beta\in\mathbb{R},$ with high exponents of smoothness $r\ (r-1\ge \sqrt{n}).$  We also obtain similar estimates for functional classes $W^r_{\beta,1}$ in metrics of the spaces $L_p, 1\le p\le\infty.$ |
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| DOI: | 10.37863/umzh.v74i5.7136 |