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Comptes Rendus Mathématique
Volume 350, n° 9-10
pages 465-467 (mai 2012)
Doi : 10.1016/j.crma.2012.05.004
Received : 24 September 2011 ;  accepted : 11 May 2012
On the singular factor of a linear combination of holomorphic functions
Sur le facteur singulier dʼune combinaison linéaire de fonctions holomorphes
 

Konstantin M. Dyakonov 1
ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007 Barcelona, Spain 

Abstract

We prove that the linear combinations of functions   have “few” singular inner factors, provided that the  ʼs are suitably smooth up to the boundary, while in general this is no longer true.

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Résumé

On démontre que les combinaisons linéaires des fonctions   possèdent « peu » de facteurs singuliers, à condition que les   soient suffisamment lisses jusquʼau bord, mais que ceci nʼest pas vrai dans le cas général.

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1  Supported in part by grant MTM2011-27932-C02-01 from El Ministerio de Ciencia e Innovación (Spain) and grant 2009-SGR-1303 from AGAUR (Generalitat de Catalunya).


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