Determinant Condition for Multi-Tiling Riesz Spectral Measure
By: Alexander Sheynis
Department: Mathematics
Faculty Advisor: Dr. Chun-Kit Lai
We establish a determinant condition that arises in the analysis of verifying Riesz spectrality for multi-tiling measures built from a finite union of finite Borel measures. This condition allows for a generalization for any such measure which adds to the body of work and exploration of various conditions or geometries for which domains admit a Riesz spectrum. We show that we recover previous major results in the work that has come before from this perspective, and open the door for how this condition may be used as a new tool in further exploration of the topic of when Riesz spectrums exist particularly with seemingly bizarre geometries.