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

页码：439 / 448

页数：10

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