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

Rita Giuliano; Georges Grekos; Ladislav Mišík

doi:10.2478/udt-2024-0005

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

Uniform distribution theory

Volume 19 (2024): Issue 1-2 (December 2024)

By: Rita Giuliano, Georges Grekos and Ladislav Mišík

Open Access

|Feb 2025

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.

References

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Articles in this issue

DOI: https://doi.org/10.2478/udt-2024-0005 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 43 - 66

Submitted on: Mar 30, 2024

Accepted on: Jul 10, 2024

Published on: Feb 24, 2025

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Beurling–Malliavin density,

upper Pólya density,

increasing sequence,

substantial interval,

Related subjects:

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2025 Rita Giuliano, Georges Grekos, Ladislav Mišík, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 19 (2024): Issue 1-2 (December 2024)