Originally Published In
Knese, Greg. Determinantal representations of semihyperbolic polynomials. Michigan Math. J. 65 (2016), no. 3, 473--487. doi:10.1307/mmj/1472066143. http://projecteuclid.org/euclid.mmj/1472066143.
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.
Knese, Greg, "Determinantal Representations of Semihyperbolic Polynomials" (2016). Mathematics Faculty Publications. 40.