= Analytic estimate for the torus cohomological equation
{title2=$\|f\|_{\sigma-\delta}\le C\gamma^{-1}\delta^{-(n+\tau)}\|g\|_\sigma$}
= Torus small-divisor estimate
{synonym}
If $g$ is analytic on a complex strip of width $\sigma$ and has zero mean, the normalized solution satisfies $\|f\|_{\sigma-\delta}\le C_{n,\tau}\gamma^{-1}\delta^{-(n+\tau)}\|g\|_\sigma$. Fourier decay supplies $e^{-\delta|k|_1}$ after the strip loss, and lattice-shell counting bounds the remaining sum $\sum_{k\ne0}|k|_1^\tau e^{-\delta|k|_1}$. This simple bound is sufficient for analytic conjugacy iterations even when sharper estimates are available.
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