Determinantal representations of semi-hyperbolic polynomials
Algebraic Geometry
2022-03-04 v2 Complex Variables
Functional Analysis
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.
Cite
@article{arxiv.1308.6556,
title = {Determinantal representations of semi-hyperbolic polynomials},
author = {Greg Knese},
journal= {arXiv preprint arXiv:1308.6556},
year = {2022}
}
Comments
14 pages, revision