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

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

thesis_v9.tex (65 kB)

Included in

Mathematics Commons

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