MINIMAL ENERGY POINT SYSTEMS ON THE UNIT CIRCLE AND THE REAL LINE

被引：1

作者：

Gaal, Marcell ^{[1
]}

Nagy, Bela ^{[2
]}

Nagy-Csiha, Zsuzsanna ^{[3
,4
]}

Revesz, Szilard Gy ^{[1
]}

机构：

[1] Alfred Renyi Inst Math, H-1053 Budapest, Hungary

[2] Univ Szeged, MTA SZTE Anal & Stochast Res Grp, H-6720 Szeged, Hungary

[3] Univ Pecs, Inst Math & Informat, Pecs, Hungary

[4] Eotvos Lorand Univ, Dept Numer Anal, H-1117 Budapest, Hungary

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2020年 / 52卷 / 06期

关键词：

Blaschke product; electrostatic equilibrium; potential theory; external fields; ELECTROSTATIC INTERPRETATION; ZEROS; POLYNOMIALS; INTERPOLATION; STIELTJES; MODEL;

D O I：

10.1137/19M1302971

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate discrete logarithmic energy problems in the unit circle. We study the equilibrium configuration of n electrons and n - 1 pairs of external protons of charge +1/2. It is shown that all the critical points of the discrete logarithmic energy are global minima, and they are the solutions of certain equations involving Blaschke products. As a nontrivial application, we refine a recent result of Simanek; namely, we prove that any configuration of n electrons in the unit circle is in stable equilibrium (that is, they are not just critical points but are of minimal energy) with respect to an external field generated by n - 1 pairs of protons.

引用

页码：6281 / 6296

页数：16

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