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Rate of convergence of Fejer kernel to the Dirac delta function
For any $\delta,x$ such that $0<\delta\leq |x|<\pi$ one has $|F_N(x)|\leq[2\pi(N+1)\sin^2(\delta/2)]^{-1}$, so the error in the delta-function approximation is of order $1/N$.
Two explicit examples, i …