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
Accessibility Statement
This item was created or digitized prior to April 24, 2027, or is a reproduction of legacy media created before that date. It is preserved in its original, unmodified state specifically for research, reference, or historical recordkeeping. In accordance with the ADA Title II Final Rule, the University Libraries provides accessible versions of archival materials upon request. To request an accommodation for this item, please submit an accessibility request form.