Approximation on limit compacta of Kleinian groups

N. A. Shirokov

Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 24, Tome 232 (1996), pp. 199-212

Résumé

Let $\Gamma$ be a geometrically finite Kleinian group, acting on $\mathbb C$, and let $\Lambda$ be the limit set of $\Gamma$, $\Omega=\mathbb C\setminus\Lambda$, $\infty\in\Omega$. Denote by $X$ either $C(\Lambda)$ or $h^\alpha(\Lambda)$, where $h^\alpha(\Lambda)=\{f\colon|f(z)-f(\zeta)|=o(|z-\zeta|^\alpha),\ z,\zeta\in\Lambda\}$. In а natural way, with the action of $\Gamma$ we relate a contable set $\Xi\subset\Omega$ and prove that $\operatorname{clos}_XL(\frac1{z-\alpha},\alpha\in\Xi)=X$. Bibl. 6 titles.