A. Grinshpan

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20122019

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math.FA2015

Contractive determinantal representations of stable polynomials on a matrix polyball

Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1

We show that an irreducible polynomial $p$ with no zeros on the closure of a matrix unit polyball, a.k.a. a cartesian product of Cartan domains of type I, and such that $p (0) = 1$ , a…

math.FA2012

Norm-constrained determinantal representations of polynomials

Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman

For every multivariable polynomial $p$ , with $p (0) = 1$ , we construct a determinantal representation $p = det (I - K Z),$ where $Z$ is a diagonal matrix with coordinate variables on…