Introducción a los Productos de Blaschke

Abstract

It is necessary to clarify that this work is focused on the de nition of a Blaschke product, its properties, its relation with Hardy spaces and a theorem that has to do with functions of Nevanlinna Class and Blaschke products. First we start with something like the previous defi nitions that will be important in the course of the same as the analytical functions, it is claried in this part that also talks about the poles and zeros of these functions. In addition to these functions, the subharmonic functions and properties of the functions are also presented, in order to later enter series and successions and types of convergence, this is done in order to access the infinite products and the equivalence between the convergence of these products and the convergence of series with a particular form, since this is the main objective of the work. Lastly, the Hardy spaces, the Nevanlinna Class functions and the Blaschke products are defined, the properties of these are shown by means of propositions, and finally the theorem that was mentioned at the beginning of this paragraph is shown.