On uniform convergence of Fourier series

Details On uniform convergence of Fourier series On uniform convergence of Fourier series

2012-03-30

arxiv.org/abs/1203.6703v1

Mathematics

Classical Analysis and ODEs

Scientific paper

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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