Estimates of deviations of Fourier sums on Weyl-Nagy classes $W^r_{β,1}$
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866916957697081344 |
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| author | Serdyuk, A. S. Sokolenko, I. V. |
| author_facet | Serdyuk, A. S. Sokolenko, I. V. |
| contents | We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{β,1}, r>2, β\in\mathbb{R},$ of $2π$-periodic functions whose $(r,β)$-derivatives in the Weyl--Nagy sense belong to the unit ball of the space $L_1$. The specified estimates allow us to write asymptotic equalities for the quantities $\sup\limits_{f\in W^r_{β,1}}|f(x)-S_{n-1}(f;x)|$ as $n\rightarrow\infty$, $r\rightarrow\infty$ for arbitrary relations between the parameters $r$ and $n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_15769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Estimates of deviations of Fourier sums on Weyl-Nagy classes $W^r_{β,1}$ Serdyuk, A. S. Sokolenko, I. V. Classical Analysis and ODEs 42A10 We establish estimates for exact upper bounds of deviations of partial Fourier sums $S_{n-1}(f)$ on classes $W^r_{β,1}, r>2, β\in\mathbb{R},$ of $2π$-periodic functions whose $(r,β)$-derivatives in the Weyl--Nagy sense belong to the unit ball of the space $L_1$. The specified estimates allow us to write asymptotic equalities for the quantities $\sup\limits_{f\in W^r_{β,1}}|f(x)-S_{n-1}(f;x)|$ as $n\rightarrow\infty$, $r\rightarrow\infty$ for arbitrary relations between the parameters $r$ and $n$. |
| title | Estimates of deviations of Fourier sums on Weyl-Nagy classes $W^r_{β,1}$ |
| topic | Classical Analysis and ODEs 42A10 |
| url | https://arxiv.org/abs/2509.15769 |