Comptes Rendus
no. 9-10
Complex Analysis/Functional Analysis
On the singular factor of a linear combination of holomorphic functions
[Sur le facteur singulier dʼune combinaison linéaire de fonctions holomorphes]

Présenté par : the Editorial Board

Konstantin M. Dyakonov1
1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007 Barcelona, Spain
Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 465-467.

On démontre que les combinaisons linéaires des fonctions f0,…,fn∈H∞ possèdent « peu » de facteurs singuliers, à condition que les fj soient suffisamment lisses jusquʼau bord, mais que ceci nʼest pas vrai dans le cas général.

We prove that the linear combinations of functions f0,…,fn∈H∞ have “few” singular inner factors, provided that the fjʼs are suitably smooth up to the boundary, while in general this is no longer true.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2012.05.004
Konstantin M. Dyakonov 1

1 ICREA and Universitat de Barcelona, Departament de Matemàtica Aplicada i Anàlisi, Gran Via 585, 08007 Barcelona, Spain 
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Konstantin M. Dyakonov. On the singular factor of a linear combination of holomorphic functions. Comptes Rendus. Mathématique, Volume 350 (2012) no. 9-10, pp. 465-467. doi : 10.1016/j.crma.2012.05.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.05.004/

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