Uniqueness theorems for Korenblum type spaces |
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Authors: | Alexander Borichev Yurii Lyubarskii |
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Institution: | (1) Centre de Mathématiques et Informatique, Université d’Aix-Marseille I, 39 rue Frédéric Joliot-Curie, 13453 Marseille, France;(2) Department of Mathematical Sciences, Norwegian University of Science and Technology, N-7491 Trondheim, Norway |
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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 ɛ of uniqueness subsets
for X, we describe minorants for (X, ɛ), that is, non-decreasing functions M: (0, 1) → (0, ∞) such that f ∈ X, E ∈ ɛ, and log |f(z)| ≤ −M(|z|) on E imply f = 0. We give an application of this result to approximation by simple fractions with restrictions on the coefficients.
The first author was partially supported by the ANR project DYNOP.
The second author was partially supported by the Research Council of Norway, grant 160192/V30. |
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