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Asymptotic Properties Of The Potentials For Greedy Energy Sequences On The Unit Circle, Ryan Edward Mccleary

Honors Undergraduate Theses

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.