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Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients

机译：具有实系数或复系数的多项式的Rolle定理的猜想类比

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摘要

Let a certain equation be a polynomial in Cz having the origin as the center of gravity of its zeros z sub j. We call another equation the quadratic radius of p sub n(z). We also consider a derivative and its quadratic radius. The main purpose of this reprint is to state that we have the inequality with the equality sign if and only all the zeros z sub j of p sub n(z) are real, or equivalently, all z sub j are on a straight line of C.

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作者
Schoenberg, I. J.;
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年度 1986
页码 p.1-4
总页数 4
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Polynomials; Coefficients; Equations; Quadratic equations; Radius(Measure); Reprints;

机译：多项式;系数;方程;二次方程;半径（测量）;重印;

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专利

1. A rolle's theorem for real exponential polynomials in the complex domain [J] . Franck Wielonsky Journal de Mathematiques Pures et Appliquees . 2001,第4期

机译：复域中实指数多项式的Rolle定理
2. Mean value theorems for polynomial solutions of linear elliptic equations with constant coefficients in the complex plane [J] . Olga D. Trofymenko Journal of Mathematical Sciences . 2021,第3期

机译：复杂平面恒系数线性椭圆方程多项式解定学的平均值定理
3. On the Zeros and Critical Points of Polynomials with Nonnegative Coefficients: A Nonconvex Analogue of the Gauss-Lucas Theorem [J] . Sendov Blagovest, Sendov Hristo Constructive approximation: An international journal for approximations and expansions . 2017,第2期

机译：非负系数多项式的零和关键点：高斯 - 卢卡斯定理的非凸起类似物
4. Polynomial Hierarchy, Betti Numbers and a Real Analogue of Toda's Theorem [C] . Basu S., Zell T. Foundations of Computer Science, 2009. FOCS '09 . 2009

机译：多项式层次结构，贝蒂数和Toda定理的实比
5. Exploring Students' Ownership of Their Conceptual Level Thinking about Sandwich Theorem, Rolle's Theorem and Mean Value Theorem in Calculus [D] . Acevedo, Carlos I. 2018

机译：探索学生对思想思路的所有权，思考Sandwich Theorem，Rolle定理和微积分的平均值定理
6. REGULARITY THEOREMS FOR SOLUTIONS OF PARTIAL DIFFERENTIAL EQUATIONS WITH VARIABLE COEFFICIENTS [O] . Felix E. Browder 1957

机译：可变系数偏微分方程解的正则定理
7. Rolle's Theorem for Complex Polynomials with Real Coefficients [O] . Sendov Blagovest 2010

机译：具有实系数的复杂多项式的罗尔定理
8. On the analogue for Maximally Convergent Polynomials of Jentzsch&s Theorem [R] . J. L. Walsh 1958

机译：关于Jentzsch定理的极大收敛多项式的模拟

Conjectured Analogue of Rolle's Theorem for Polynomials with Real or Complex Coefficients

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