Author's School

Arts & Sciences

Author's Department

Mathematics

Document Type

Article

Publication Date

8-24-2016

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.

Abstract

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.

Comments

Final published version posted with permission from Michigan Matheematical Journal.

doi:10.1307/mmj/1472066143

http://projecteuclid.org/euclid.mmj/1472066143.

DOI

10.1307/mmj/1472066143

Included in

Mathematics Commons

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