Vojkan Jaksic and Stanislav Molchanov
A Note on the Regularity of  Solutions of  Linear 
Homological Equations 
(384K, postscript)

ABSTRACT.  We study the linear homological equation $\mu(t+ 2\pi\gamma) -\mu(t) = 
\nu(t)$ on the circle ${\bf T}$. 
We show that if the Fourier coefficients of $\nu$ 
satisfy ${\hat \nu}(n) = 
O(\vert n \vert^{-1 - \alpha})$ for some $0 < \alpha \leq 1$, 
then for Lebesgue a.e. $\gamma \in (0,1)$ the solution $\mu$ belongs to 
${\rm Lip}_{\alpha^\prime}({\bf T})$ for any $\alpha^\prime < \alpha$.