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A relative Grace Theorem for complex polynomials

Published online by Cambridge University Press:  11 February 2016

DANIEL PLAUMANN  and
MIHAI PUTINAR
DANIEL PLAUMANN
Affiliation:
Zukunftskolleg and Fachbereich Mathematik, Box 216, Universität Konstanz, 78457 Konstanz, Germany e-mail: [email protected]
MIHAI PUTINAR
Affiliation:
Department of Mathematics, University of California at Santa Barbara, Santa Barbara, CA 93106-3080, U.S.A. School of Mathematics & Statistics, Newcastle University, Newcastle upon Tyne, NE1 7RU, U.K. e-mail: [email protected], [email protected]
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Abstract

We study the pullback of the apolarity invariant of complex polynomials in one variable under a polynomial map on the complex plane. As a consequence, we obtain variations of the classical results of Grace and Walsh in which the unit disk, or a circular domain, is replaced by its image under the given polynomial map.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 1 , July 2016 , pp. 17 - 30
Copyright
Copyright © Cambridge Philosophical Society 2016 

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