The Beurling-Malliavin Density, The Pólya Density and Their Connection

Abstract In this paper we analyze the Beurling-Malliavin density and some other quantities related to it. Then we consider the upper Pólya density and show how its existence is connected with the concept of subadditivity; moreover a theorem is presented that clarifies the connection between the upper Pólya and the Beurling-Malliavin densities. In the last section we discuss the classical definition of the upper Pólya density and we prove a result which seems to be new.