Publication Date

Summer 7-28-2026

Abstract

The Heisenberg uncertainty principle is a central aspect of quantum mechanics, but also illustrates an essential quality of the Fourier transform. After Heisenberg, a variety of uncertainty inequalities emerged in the fields of physics and mathematics. In this thesis we will analyze the Heisenberg uncertainty principle in both the setting of quantum mechanics and Fourier analysis. We will then look at how the work of Heisenberg has been expanded upon in both physics and mathematics. Particularity, we will see how uncertainty principles can be applied to signal recovery and explore current research in this field.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

Maria Cristina Pereyra

Second Committee Member

Mathew Blair

Third Committee Member

Owen Lewis

Language

English

Keywords

Fourier Analysis, Hiesenberg, Donoho-Stark, Entropy

Document Type

Thesis

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