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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.
Research in the Mathematical Sciences – Springer Journals
Published: May 15, 2018
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