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arXiv · 1308.6556

Determinantal representations of semi-hyperbolic polynomials

Greg Knese
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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.

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Greg Knese. 2013-08-29. Determinantal representations of semi-hyperbolic polynomials. https://doi.org/10.1307/mmj%2F1472066143

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