00-94 Vojkan Jaksic and Stanislav Molchanov
A Note on the Regularity of Solutions of Linear Homological Equations (384K, postscript) Feb 29, 00
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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 $\alpha^\prime < \alpha$.

Files: 00-94.ps