A generalization of the Beurling--Malliavin Majorant theorem

TL;DR

This paper generalizes the Beurling--Malliavin Majorant Theorem by providing a new, more inclusive sufficient condition for functions to qualify as Majorants, demonstrating the result's sharpness in various aspects.

Contribution

It introduces a broader sufficient condition for Beurling--Malliavin Majorants, extending the classical theorem and establishing the sharpness of this new criterion.

Findings

New sufficient condition for Majorants

Generalization of the classical theorem

Proof of the sharpness of the result

Abstract

In this article we prove a generalization of the Beurling--Malliavin Majorant Theorem. In more detail, we establish a new sufficient condition for a function to be a Beurling--Malliavin Majorant. Our result is strictly more general than that of the Beurling--Malliavin Majorant Theorem. We also show that our result is sharp in a number senses.