Abstract:
The following result is proved:
THEOREM: {\it Let $S$ be an inner function, $\operatorname{spec}S\subset E$, $E\subset\operatorname{clos}\mathbb D$. Suppose $E$ satisfies
$$
\sum_{\alpha\in\mathbb D\cap E}(1-|\alpha|)<\infty,\quad\int_{\partial\mathbb D}\log\omega(\operatorname{dist}(z,E))|dz|>-\infty,
$$ $\omega$ being a continuity modulus. Then there exists a function $\Lambda_\omega$ such that $f^{-1}(0)\in E$ è $f|_S\in\Lambda_\omega$}.
Fulltext:
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