 0094 Vojkan Jaksic and Stanislav Molchanov
 A Note on the Regularity of Solutions of Linear
Homological Equations
(384K, postscript)
Feb 29, 00

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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 $\alpha^\prime < \alpha$.
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