Cauchy-de Branges空间中的零点局部化
复变函数
2022-06-29 v2 泛函分析
摘要
我们研究复平面上离散测度的一类性质：除有限个外，该测度的任意Cauchy变换（具有-数据）的所有零点都局部化于测度支撑集附近。我们给出了该性质的几种等价形式，并证明吸引Cauchy变换零点的支撑集部分在模有限集包含意义下有序。
引用
@article{arxiv.2206.13376,
title = {Localization of zeros in Cauchy-de Branges spaces},
author = {Evgeny Abakumov and Anton Baranov and Yurii Belov},
journal= {arXiv preprint arXiv:2206.13376},
year = {2022}
}
备注
This paper is a continuation of arXiv:1312.6706. It extends the results obtained in arXiv:1312.6706 for the Cauchy transforms of measures with support on the real line to the case of general discrete measures in the plane. A new elementary proof of the ordering theorem for attraction sets is given which does not use the de Branges theory and the estimates of subharmonic functions due to Heins