Physical Sciences and Mathematics Commons^™

Fuglede's Conjecture In Some Finite Abelian Groups, Thomas Fallon

Dissertations, Theses, and Capstone Projects

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.