Extention of Apolarity and Grace Theorem

Sendov, Blagovest, and Sendov, Hristo. "Extention of Apolarity and Grace Theorem." Mathematica Balkanica New Series 27.1-2 (2013): 77-87. <http://eudml.org/doc/281447>.

@article{Sendov2013,
abstract = {MSC 2010: 30C10The 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.},
author = {Sendov, Blagovest, Sendov, Hristo},
journal = {Mathematica Balkanica New Series},
keywords = {zeros and critical points of polynomials; apolarity; polar derivative; Grace theorem; zeros of polynomials; critical points of polynomials},
language = {eng},
number = {1-2},
pages = {77-87},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {Extention of Apolarity and Grace Theorem},
url = {http://eudml.org/doc/281447},
volume = {27},
year = {2013},
}

TY - JOUR
AU - Sendov, Blagovest
AU - Sendov, Hristo
TI - Extention of Apolarity and Grace Theorem
JO - Mathematica Balkanica New Series
PY - 2013
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 27
IS - 1-2
SP - 77
EP - 87
AB - MSC 2010: 30C10The 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.
LA - eng
KW - zeros and critical points of polynomials; apolarity; polar derivative; Grace theorem; zeros of polynomials; critical points of polynomials
UR - http://eudml.org/doc/281447
ER -