Nevanlinna class, Dirichlet series and Szeg\"o's problem
Complex Variables
2022-06-02 v2 Functional Analysis
Abstract
This paper is associated with Nevanlinna class, Dirichlet series and Szeg\"o'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 Szeg\"o'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.
Cite
@article{arxiv.2201.01993,
title = {Nevanlinna class, Dirichlet series and Szeg\"o's problem},
author = {Kunyu Guo and Jiaqi Ni and Qi Zhou},
journal= {arXiv preprint arXiv:2201.01993},
year = {2022}
}
Comments
Some new results are included in this version