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arXiv · 1203.6703

On uniform convergence of Fourier series

Vladimir Lebedev
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Abstract

We consider the space $U(\mathbb T)$ of all continuous functions on the circle $\mathbb T$ with uniformly convergent Fourier series. We show that if $\varphi: \mathbb T\rightarrow\mathbb T$ is a continuous piecewise linear but not linear map, then $\|e^{in\varphi}\|_{U(\mathbb T)}\simeq\log n$.

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Vladimir Lebedev. 2012-03-30. On uniform convergence of Fourier series. https://doi.org/10.1134/s0001434612050379

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