Determinantal representations of semi-hyperbolic polynomials

Abstract

We prove a generalization of the Hermitian version of the Helton-Vinnikov determinantal representation of hyperbolic polynomials to the class of semi-hyperbolic 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.

14 pages, revision

References in corpus (4)

• The Lax conjecture is true
• Hyperbolic polynomials, interlacers, and sums of squares
• Determinantal Representations and Bézoutians
• Polynomials with no zeros on a face of the bidisk

Cited by in corpus (2)

• Integrability and regularity of rational functions
• Global bounds on stable polynomials