Knese, Greg Determinantal representations of semihyperbolic polynomials. (English) Zbl 1454.14137 Mich. Math. J. 65, No. 3, 473-487 (2016). 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. Cited in 2 Documents 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 PDFBibTeX XMLCite \textit{G. Knese}, Mich. Math. J. 65, No. 3, 473--487 (2016; Zbl 1454.14137) Full Text: DOI arXiv