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Duality between loci of complex polynomials and the zeros of polar derivatives

Published online by Cambridge University Press:  12 April 2018

BLAGOVEST SENDOV  and
HRISTO SENDOV
BLAGOVEST SENDOV
Affiliation:
Bulgarian Academy of Sciences, Institute of Information and Communication Technologies, Acad. G. Bonchev Str., bl. 25A, 1113 Sofia, Bulgaria. e-mail: acad@sendov.com
HRISTO SENDOV
Affiliation:
Department of Statistical and Actuarial Sciences, Western University, 1151 Richmond Str., London, ON, N6A 5B7, Canada. e-mail: hssendov@stats.uwo.ca
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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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 167 , Issue 1 , July 2019 , pp. 65 - 87
Copyright
Copyright © Cambridge Philosophical Society 2018 

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Footnotes

†

Partially supported by Bulgarian National Science Fund #DTK 02/44.

‡

Partially supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada.

References

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