Convergence of Fourier series of functions $\text{Lip} 1$ with respect to general orthonormal systems
We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) $\{ \varphi_n(x)\}$ in order that the Fourier series in this system for any function from the class $\mathrm{L}\mathrm{i}\mathrm{p} 1$ be convergent almost everywhere on $[0, 1]$. It is sho...
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| Date: | 2017 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2017
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1710 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | We establish sufficient conditions that should be satisfied by functions of a general orthonormal system (ONS) $\{ \varphi_n(x)\}$
in order that the Fourier series in this system for any function from the class $\mathrm{L}\mathrm{i}\mathrm{p} 1$ be convergent almost everywhere on
$[0, 1]$. It is shown that the obtained conditions are best possible in a certain sense. |
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