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Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions

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We study the possibility of splitting any bounded analytic function $f$ with singularities in a closed set $E\cup F$ as a sum of two bounded analytic functions with singularities in $E$ and $F$ respectively. We obtain some results under geometric restrictions on the sets $E$ and $F$ and we provide some examples showing the sharpness of the positive results.

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Journal d'Analyse Mathematique, 2007, vol. 101, num. 1, p. 65-93

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(c) The Hebrew University of Jerusalem, 2007

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Articles publicats en revistes (Matemàtiques i Informàtica)

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Uniform estimates in the Poincare-Aronszajn theorem on the separation of singularities of analytic functions