2 citations · 2 across the 5 of their papers we have counts for
6 papers
A Linear-algebraic Proof of Hilbert's Ternary Quartic Theorem
Anatolii Grinshpan, Hugo J. Woerdeman
Hilbert's ternary quartic theorem states that every nonnegative degree 4 homogeneous polynomial in three variables can be written as a sum of three squares of homogeneous quadratic…
Rational inner functions on a square-matrix polyball
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1
We establish the existence of a finite-dimensional unitary realization for every matrix-valued rational inner function from the Schur--Agler class on a unit square-matrix polyball.…
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 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 , a…
Matrix-valued Hermitian Positivstellensatz, lurking contractions, and contractive determinantal representations of stable polynomials
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1
We prove that every matrix-valued rational function , which is regular on the closure of a bounded domain in and which has the associated…
Stable and real-zero polynomials in two variables
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov +1
For every bivariate polynomial of bidegree , with , which has no zeros in the open unit bidisk, we construct a determinantal representation of t…
Norm-constrained determinantal representations of polynomials
Anatolii Grinshpan, Dmitry S. Kaliuzhnyi-Verbovetskyi, Hugo J. Woerdeman
For every multivariable polynomial , with , we construct a determinantal representation where is a diagonal matrix with coordinate variables on…