On a Schoenberg-type conjecture

被引：6

作者：

de Bruin, MG

Sharma, A

机构：

[1] Delft Univ Technol, Fac Informat Technol & Syst, Dept Tech Math & Informat, NL-2600 GA Delft, Netherlands

[2] Univ Alberta, Dept Math Sci, Edmonton, AB T6G 2G1, Canada

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1999年 / 105卷 / 1-2期

关键词：

geometry of zeros; weighted sums; inequalities;

D O I：

10.1016/S0377-0427(99)00013-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For an arbitrary polynomial P-n(z) = z(n) - a(1)z(n-1) + a(2)z(n-2) + ... + (-1)(n)a(n) = Pi(1)(n)(z - z(j)) with the sum of all zeros equal to zero, a(1) = Sigma(1)(n) z(j) = 0, the quadratic mean radius is defined by [GRAPHICS] and the quartic mean radius by [GRAPHICS] This paper studies a Schoenberg-type conjecture using the quartic mean radius in the following form: n-4/n-1S(P-n)(4) + 2/n-1 R(P-n)(4) greater than or equal to S(P-n')(4), with equality if and only if the zeros all lie on a straight line through the origin in the complex plane. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：221 / 228

页数：8