= Fejér summation is a uniform-norm contraction
{c}
{title2=$\|\sigma_n f\|_\infty\le\|f\|_\infty$}
= Uniform-norm contraction of Fejér summation
{synonym}
The <Fejér kernel> is nonnegative and has unit mass in its convolution normalization. The integral triangle inequality therefore bounds the <supremum norm> of a <Fejér sum> by that of the original function. In the half-kernel convention $F_n=(2n)^{-1}|\sum_{j=0}^{n-1}e^{ijt}|^2$, its integral is $\pi$ and the convolution prefactor is $1/\pi$.
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