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Title: Extention of Apolarity and Grace Theorem
Authors: Sendov, Blagovest
Sendov, Hristo
Keywords: zeros and critical points of polynomials
polar derivative
Grace theorem
Issue Date: 2013
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 27, Fasc 1-2 (2013), 77p-87p
Abstract: The classical notion of apolarity is defined for two algebraic polynomials of equal degree. The main property of two apolar polynomials p and q is the classical Grace theorem: Every circular domain containing all zeros of p contains at least one zero of q and vice versa. In this paper, the definition of apolarity is extended to polynomials of different degree and an extension of the Grace theorem is proved. This leads to simplification of the conditions of several well-known results about apolarity.
Description: MSC 2010: 30C10
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 27, 2013, Fasc. 1-2

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