Abstract
In this work, we analyze the asymptotic behavior of the minimum values of Riesz s-potentials generated by greedy s-energy sequences on the unit circle. The analysis is broken into the cases 0 < s < 1, s = 1, and s > 1, since the behavior of the minimum values of the Riesz s-potential undergoes a sharp transition at s = 1. For 0 < s < 1, the first-order behavior is already known. We obtain first-order asymptotic results for 0 < s < 1. We also prove first-order and second-order asymptotic formulas for s = 1 and investigate the first-order behavior for s > 1.
Thesis Completion
2021
Semester
Spring
Thesis Chair/Advisor
Lopez-Garcia, Abey
Co-Chair
Jenkins, Robert
Degree
Bachelor of Science (B.S.)
College
College of Sciences
Department
Mathematics
Degree Program
Mathematics
Language
English
Access Status
Open Access
Release Date
5-1-2021
Recommended Citation
McCleary, Ryan Edward, "Asymptotic Properties of The Potentials For Greedy Energy Sequences On The Unit Circle" (2021). Honors Undergraduate Theses. 927.
https://stars.library.ucf.edu/honorstheses/927