A Note on the Maximum Number of Zeros of r(z) - (z)over-bar

被引：0
|
作者：
Luce, Robert [1 ]
Sete, Olivier [1 ]
Liesen, Joerg [1 ]
机构：
[1] Tech Univ Berlin, D-10623 Berlin, Germany
来源：
COMPUTATIONAL METHODS AND FUNCTION THEORY | 2015年 / 15卷 / 03期
关键词：
Complex valued harmonic function; Rational function; Zeros of rational harmonic functions;
D O I：
10.1007/s40315-015-0110-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
An important theorem of Khavinson and Neumann (Proc. Am. Math. Soc. 134: 1077-1085, 2006) states that the complex harmonic function r(z)-(z) over bar, where r is a rational function of degree n >= 2, has at most 5(n-1) zeros. In this note, we resolve a slight inaccuracy in their proof and in addition we show that for certain functions of the form r (z)-(z) over bar no more than 5(n-1)-1 zeros can occur. Moreover, we show that r (z)-(z) over bar is regular, if it has the maximal number of zeros.
引用
收藏
页码：439 / 448
页数：10
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