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

Research paper by V. P. Havin, A. H. Nersessian, J. Ortega-Cerdà

Indexed on: 01 Mar '07Published on: 01 Mar '07Published in: Journal d'Analyse Mathématique


We study the possibility of splitting any bounded analytic function ƒ with singularities in a closed set E ⋃ 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.