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Determinantal representations of semihyperbolic polynomials. (English) Zbl 1454.14137

Summary: We prove a generalization of the Hermitian version of the Helton-Vinnikov determinantal representation for hyperbolic polynomials to the class of semihyperbolic polynomials, a strictly larger class, as shown by an example. We also prove that certain hyperbolic polynomials affine in two out of four variables divide a determinantal polynomial. The proofs are based on work related to polynomials with no zeros on the bidisk and tridisk.

MSC:

14P10 Semialgebraic sets and related spaces
90C22 Semidefinite programming
15A15 Determinants, permanents, traces, other special matrix functions
47A57 Linear operator methods in interpolation, moment and extension problems
90C25 Convex programming
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