On the singular factor of a linear combination of holomorphic functions

Dyakonov, Konstantin M.

doi:10.1016/j.crma.2012.05.004

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

Dyakonov, Konstantin M.¹

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

Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 465-467.

Résumé
Abstract

On démontre que les combinaisons linéaires des fonctions $f_{0}, \dots, f_{n} \in H^{\infty}$ possèdent « peu » de facteurs singuliers, à condition que les $f_{j}$ soient suffisamment lisses jusquʼau bord, mais que ceci nʼest pas vrai dans le cas général.

We prove that the linear combinations of functions $f_{0}, \dots, f_{n} \in H^{\infty}$ have “few” singular inner factors, provided that the $f_{j}$ ʼs are suitably smooth up to the boundary, while in general this is no longer true.

Reçu le : 2011-09-24
Accepté le : 2012-05-11
Publié le : 2012-05-01

DOI : 10.1016/j.crma.2012.05.004

Affiliations des auteurs :

Dyakonov, Konstantin M. ¹

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

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Dyakonov, Konstantin M. On the singular factor of a linear combination of holomorphic functions. Comptes Rendus. Mathématique, Tome 350 (2012) no. 9-10, pp. 465-467. doi : 10.1016/j.crma.2012.05.004. http://www.numdam.org/articles/10.1016/j.crma.2012.05.004/

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