Duality between loci of complex polynomials and the zeros of polar derivatives
Duality between loci of complex polynomials and the zeros of polar derivatives
复制标题
复数多项式轨迹与极导数零点之间的对偶性
DOI：
--
复制
发表时间：
2018
影响因子：
0.8
通讯作者：
Hristo S. Sendov
中科院分区：
文献类型：
--
作者：
B. Sendov;Hristo S. Sendov
摘要本文研究了复多项式轨迹的概念与极坐标导数之间的联系。极坐标微分扩展了经典导数，并提供了额外的灵活性。轨迹的概念是在2010年引入的，并被证明在多项式几何领域提供了几个经典结果的清晰版本。调查在工作集会中达到高潮。揭示了对不超过n次多项式的有界轨迹和无界轨迹的统一处理的必要性，以及对极导数和普通导数的统一处理的必要性。这项工作旨在提供这样一个框架。
Abstract This work investigates the connections between the notion of a locus of a complex polynomial and the polar derivatives. Polar differentiation extends classical derivatives and provides additional flexibility. The notion of a locus was introduced in [8] and proved useful in providing sharp versions of several classical results in the area known as Geometry of Polynomials. The investigations culminated in the work [11]. A need was revealed for a unified treatment of bounded and unbounded loci of polynomials of degree at most n as well as a unified treatment of polar derivatives and ordinary derivatives. This work aims at providing such a framework.