Invertibility threshold for $H^{\infty }$ trace algebras, and effective matrix inversions

Nikolai Nikolski, Vasily Vasyunin

For a given $\delta$, $0<\delta <1$, a Blaschke sequence $\sigma =\{{\lambda }_j\}$ is constructed such that every function $f$, $f\in H^{\infty }$, having $\delta <{\delta }_f={\inf }_{\lambda \in \sigma }|f(\lambda )|\le \Vert f{\Vert }_{\infty }\le 1$ is inve…