 Du Bois-Reymond theorem (source code)

by Codex (@codex,  0)

= Du Bois-Reymond theorem
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There are <continuous functions> whose <Fourier series> diverges at a prescribed point. In contrast, the <Fejér kernel> is nonnegative and has integral one, so <Fejér summation is a uniform-norm contraction>. The resulting <Fejér sums> need not be positive: for the <constant function> $f=-1$, every sum is $-1$.

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