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Conic stability of polynomials

Conic stability of polynomials We introduce and study the notion of conic stability of multivariate complex polynomials in $$\mathbb {C}[\mathbf {z}]$$ C [ z ] , which naturally generalizes the stability of multivariate polynomials. In particular, we generalize Borcea’s and Brändén’s multivariate version of the Hermite–Kakeya–Obreschkoff Theorem to the conic stability and provide a characterization in terms of a directional Wronskian. And we generalize a major criterion for stability of determinantal polynomials to stability with respect to the positive semidefinite cone. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

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References (34)

Publisher
Springer Journals
Copyright
Copyright © 2018 by SpringerNature
Subject
Mathematics; Mathematics, general; Applications of Mathematics; Computational Mathematics and Numerical Analysis
eISSN
2197-9847
DOI
10.1007/s40687-018-0144-2
Publisher site
See Article on Publisher Site

Abstract

We introduce and study the notion of conic stability of multivariate complex polynomials in $$\mathbb {C}[\mathbf {z}]$$ C [ z ] , which naturally generalizes the stability of multivariate polynomials. In particular, we generalize Borcea’s and Brändén’s multivariate version of the Hermite–Kakeya–Obreschkoff Theorem to the conic stability and provide a characterization in terms of a directional Wronskian. And we generalize a major criterion for stability of determinantal polynomials to stability with respect to the positive semidefinite cone.

Journal

Research in the Mathematical SciencesSpringer Journals

Published: May 15, 2018

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