The Beurling-Malliavin density, the Polya density and their connection

TL;DR

This paper introduces a new formulation of the Beurling-Malliavin density, explores its connection with the Polya density, and presents new results clarifying their relationship and properties.

Contribution

It provides a novel formulation of the Beurling-Malliavin density and establishes new links between the upper Polya density and the Beurling-Malliavin density.

Findings

New formulation of Beurling-Malliavin density

Connection between upper Polya and Beurling-Malliavin densities

A potentially new result on the classical upper Polya density

Abstract

In this paper we present a new formulation of the Beurling-Malliavin density (Proposition 1). Then we consider the upper Polya density and show how its existence is connected with the concept of subadditivity; moreover, by means of some quantities introduced for proving Proposition 1, a theorem is presented that clarifies the connection between the upper Polya and the Beurling-Malliavin densities. In the last section we discuss the classical definition of the upper Polya density and we prove a result which seems to be new.