Periodic Korovkin test set
= Periodic Korovkin test set
{title2=$\{1,\sin x,\cos x\}$}
For $2\pi$-periodic <continuous functions>, convergence of <positive linear operators on continuous functions> to the identity on $1,\sin x,\cos x$ implies <uniform convergence> on every function. Indeed $1-\cos(t-x)$ is nonnegative and has just one zero on the circle, so the <compact Korovkin test space> criterion applies.