= Fejér-kernel proof of the analytic large sieve
{c}
A triangular taper majorizes a fixed fraction of the summation interval. Its Fourier kernel is the <Fejér kernel>, bounded by $C\min(m,(m\|\theta\|^2)^{-1})$. For separated sample points, split each row sum at distance $1/m$: the plateau and square-decay tail each contribute $O(\delta^{-1})$, while the diagonal contributes $O(m)$. Bounding the resulting <quadratic form> proves the dual sieve with constant $C(N+\delta^{-1})$. <Operator norm duality> gives the primal sieve.
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