Families of Newton-like inequalities for sets of self-conjugate complex numbers

We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first known inequalities of this type which are independent of the proximity of the complex numbers to the real axis.

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Bibliographic Details
Published in:Linear algebra and its applications 2020-07, Vol.597, p.46-68
Main Authors: Ellard, Richard, Šmigoc, Helena
Format: Article
Language:English
Subjects:
Complex numbers
Conjugates
Elementary symmetric functions
Hermite-Biehler Theorem
Hurwitz matrix
Inequalities
Linear algebra
Newton's inequalities
λ-Newton inequalities
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Description
Summary:We derive families of Newton-like inequalities involving the elementary symmetric functions of sets of self-conjugate complex numbers in the right half-plane. These are the first known inequalities of this type which are independent of the proximity of the complex numbers to the real axis.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.03.014