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Uniqueness theorems for Korenblum type spaces

Alexander Borichev·Yurii Lyubarskii
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Abstract

For a scale of spaces $X$ of functions analytic in the unit disc, including the Korenblum space, and for some natural families $\mathcal E$ of uniqueness subsets for $X$, we describe minorants for $(X,\mathcal E)$, that is non-decreasing functions $M:(0,1)\to(0,\infty)$ such that $f\in X$, $E\in\mathcal E$, and $\log|f(z)|\le -M(|z|)$ on $E$ imply $f=0$. We give an application of this result to approximation by simple fractions with restrictions on the coefficients.

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Alexander Borichev, Yurii Lyubarskii. 2005-12-18. Uniqueness theorems for Korenblum type spaces. https://arxiv.org/abs/math/0512425

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