Asymptotics of the Energy of Sections of Greedy Energy Sequences on the Unit Circle, and Some Conjectures for General Sequences

作者：Lopez Garcia Abey^*; Wagner Douglas A

来源：Computational Methods and Function Theory, 2015, 15(4): 721-750.

DOI：10.1007/s40315-015-0140-0

• Greedy energy sequence
• Leja sequence
• Riesz kernel
• Equilibrium measure
• Optimal energy configuration

In this paper we investigate the asymptotic behavior of the Riesz s-energy of the first N points of a greedy s-energy sequence on the unit circle, for all values of s in the range 0 <= s < infinity (identifying as usual the case s = 0 with the logarithmic energy). In the context of the unit circle, greedy s-energy sequences coincide with the classical Leja sequences constructed using the logarithmic potential. We obtain first-order and second-order asymptotic results. The key idea is to express the Riesz s-energy of the first N points of a greedy s-energy sequence in terms of the binary representation of N. Motivated by our results, we pose some conjectures for general sequences on the unit circle.

• 出版日期2015-12