= Cohomological equation on a Diophantine torus
{title2=$\mathcal D_\omega f=g$}
= Cohomological equations on a Diophantine torus
{synonym}
For a <Diophantine frequency vector>, the equation $\omega\cdot\partial_x f=g$ on a periodic <torus> has an analytic solution on each smaller complex strip exactly when $g$ has zero average. Its nonzero <Fourier coefficients> are $f_k=g_k/(i k\cdot\omega)$, and its zero coefficient is arbitrary. Thus the normalized zero-mean solution is unique.
Back to article page
