The number of zeros of a sum of fractional powers

被引：0

作者：

James, GJO ^{[1
]}

机构：

[1] Univ Lancaster, Dept Math & Stat, Lancaster LA1 4YF, England

来源：

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 2006年 / 462卷 / 2070期

关键词：

zeros; Descartes; Laguerre; sign changes; exponential sums;

D O I：

10.1098/rspa.2005.1647

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider functions of the form f(x) Sigma(n)(j=1) c(j)(x + a(j))(p) where a(1) > center dot center dot center dot > a(n) >= 0. A version of Descartes's rule of signs applies. Further, if C-j, = Sigma(j)(i=1) and C-n = 0. then the number of zeros of f is bounded by the number of sign changes of ( C-j). The estimate is reduced by 1 for each relation of the form Sigma(n)(j=1) c(j)a(j)(r) = 0.

引用

页码：1821 / 1830

页数：10