The logarithmic energy of zeros and poles of a rational function

被引：0
作者：
V. N. Dubinin
机构：
[1] Far-Eastern Federal University,
[2] Institute of Applied Mathematics,undefined
来源：
Siberian Mathematical Journal | 2016年 / 57卷
关键词：
rational function; Zolotarev fraction; lemniscate; logarithmic energy;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
On assuming that certain lemniscates of a rational function are connected, we establish some sharp inequality that involves the logarithmic energy of a discrete charge concentrated at the zeros and poles of this function and the absolute values of its derivatives at these points. The equality in this estimate is attained for specially arranged zeros and poles of a suitable Zolotarev fraction and for special distributions of charge.
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页码：981 / 986
页数：5
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  • [6] Dubinin V. N.(undefined)undefined undefined undefined undefined-undefined
  • [7] Bogatyrev A. B.(undefined)undefined undefined undefined undefined-undefined
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