On point-mass Riesz external fields on the real axis

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:491

Article

Benko, D.¹  Dragnev, P. D.²  Orive, R.³ 

[1] Aldas Sch, Budapest, Hungary

[2] Purdue Univ, Dept Math Sci, Ft Wayne, IN 46805 USA

[3] Univ La Laguna, Dept Anal Matemat, Canary Isl, Spain

关键词: Riesz energy;    Equilibrium measures;    External fields;    Balayage;   

DOI  :  10.1016/j.jmaa.2020.124299

来源: Elsevier

【 摘 要 】

The purpose of this work is twofold. First, we aim to extend for 0 < s < 1 the results of one of the authors about equilibrium measures in the real axis in external fields created by point-mass charges for the case of logarithmic potentials (s = 0). Our second motivation comes from the work of the other two authors on Riesz s-equilibrium problems on finitely many intervals on the real line in the presence of external fields. They have shown that when the signed equilibrium measure has concave positive part on every interval, then the s-equilibrium support is also a union of finitely many intervals, with one of them at most included in each of the initial intervals. As the positive part of the signed equilibrium for point-mass external fields is not necessarily concave, the investigation of the corresponding s-equilibrium support is of comparative interest. Moreover, we provide simple examples of compactly supported equilibrium measures in external fields Q not satisfying the usual requirements about the growth at infinity, that is, lim(vertical bar x vertical bar -> infinity )Q(x) = infinity. Our main tools are signed equilibrium measures and iterated balayage algorithm in the context of Riesz s-equilibrium problems on the real line. As these techniques are not mainstream work in the field and can be applied in other contexts we highlight their use here. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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