Spring 2019

Elementary Derivation of Hermitian Determinantal Representations for Trivariate Hyperbolic Polynomials

Wednesday, Feb. 27, 2019 10:30 am12:00 pm PST

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Nick Ryder


Room 116

In the paper "Stable and Real-Zero Polynomials in Two-Variables" by Grinshpan, Kaliuzhnyi-Verbovetskyi, Vinnikov, Woerdeman, they reduce constructing a Hermitian determinantal representation for trivariate hyperbolic polynomials to constructing a certain factorization of a positive definite valued matrix polynomial. I will present this derivation and then present an elementary proof of the existence of these factorizations following the paper "A Simple Proof of the Matrix-Valued Fejer-Riesz Theorem" by Ephremidze, Janashia, and Lagvilava.