Nevanlinna class, Dirichlet series and Szegő’s problem
[Classe Nevanlinna, série Dirichlet et problème de Szegö]
Guo, Kunyu1 ; Ni, Jiaqi2 ; Zhou, Qi3
1 School of Mathematical Sciences, Fudan University, Shanghai (China)
2 School of Mathematics and Statistics, Northeast Normal University, Changchun (China)
3 School of Mathematical Sciences, Soochow University, Suzhou (China)
Annales de l'Institut Fourier, Online first, 45 p.

Cet article est associé à la classe de Nevanlinna, aux séries de Dirichlet et au problème de Szegő en un nombre infini de variables. Comme nous le verrons, il existe une connexion naturelle entre ces sujets. L’article introduit d’abord la classe de Nevanlinna et la classe de Smirnov dans ce contexte, et généralise la théorie classique en un nombre fini de variables au cadre des variables infinies. Ces résultats sont ensuite appliqués au problème de Szegő dans les espaces de Hardy en un nombre infini de variables. De plus, cet article est également consacré à l’étude de la correspondance entre les fonctions de Nevanlinna et les séries de Dirichlet.

This paper is associated with Nevanlinna class, Dirichlet series and Szegő’s problem in infinitely many variables. As we will see, there is a natural connection between these topics. The paper first introduces the Nevanlinna class and the Smirnov class in this context, and generalizes the classical theory in finitely many variables to the infinite-variable setting. These results applied to Szegő’s problem on Hardy spaces in infinitely many variables. Moreover, this paper is also devoted to the study of the correspondence between the Nevanlinna functions and Dirichlet series.

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DOI : 10.5802/aif.3696
Classification : 30B50, 30H15, 46E50
Keywords: Nevanlinna class, Smirnov class, Dirichlet series, Szegő’s problem, infinitely many variables
Mots-clés : classe Nevanlinna, classe Smirnov, série Dirichlet, le problème de Szegö, une infinité de variables

Guo, Kunyu 1 ; Ni, Jiaqi 2 ; Zhou, Qi 3

1 School of Mathematical Sciences, Fudan University, Shanghai (China)
2 School of Mathematics and Statistics, Northeast Normal University, Changchun (China)
3 School of Mathematical Sciences, Soochow University, Suzhou (China) 
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Guo, Kunyu; Ni, Jiaqi; Zhou, Qi. Nevanlinna class, Dirichlet series and Szegő’s problem. Annales de l'Institut Fourier, Online first, 45 p.

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