Fuglede's Conjecture in Some Finite Abelian Groups

Author

Thomas Fallon, The Graduate Center, City University of New YorkFollow

Date of Degree

9-2023

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Azita Mayeli

Committee Members

Krzystof Klosin

Olga Kharlampovich

Gábor Somlai

Subject Categories

Discrete Mathematics and Combinatorics | Harmonic Analysis and Representation

Keywords

spectral sets, tiling sets, fourier transform

Abstract

This dissertation thoroughly examines Fuglede's Conjecture within some discrete settings, shedding light on its intricate details. Fuglede's Conjecture establishes a profound connection between the geometric property of being a tiling set and the analytical attribute of being a spectral set. By exploring the conjecture on various discrete settings, this thesis delves into the implications and ramifications of the conjecture, unraveling its implications within the field.

Recommended Citation

Fallon, Thomas, "Fuglede's Conjecture in Some Finite Abelian Groups" (2023). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/5542