Nevanlinna class, Dirichlet series and Szeg\"o's problem

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.