38 citations · 43 across the 15 of their papers we have counts for
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Integrability of Free Noncommutative Functions
Dmitry Kaliuzhnyi-Verbovetskyi, Leonard Stevenson, Victor Vinnikov
Noncommutative functions are graded functions between sets of square matrices of all sizes over two vector spaces that respect direct sums and similarities. They possess very stron…
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…
Scattering systems with several evolutions and formal reproducing kernel Hilbert spaces
Joseph A. Ball, Dmitry Kaliuzhnyi-Verbovetskyi, Cora Sadosky +1
A Schur-class function in variables is defined to be an analytic contractive-operator valued function on the unit polydisk. Such a function is said to be in the Schur--Agler cl…
Rational Cayley inner Herglotz-Agler functions: positive-kernel decompositions and transfer-function realizations
Joseph A. Ball, Dmitry S. Kaliuzhnyi-Verbovetskyi
The Bessmertny\uı class consists of rational matrix-valued functions of complex variables representable as the Schur complement of a block of a linear pencil $A(z)=z_1A_1+\cdot…
Schur--Agler and Herglotz--Agler classes of functions: positive-kernel decompositions and transfer-function realizations
Joseph A. Ball, Dmitry S. Kaliuzhnyi-Verbovetskyi
We discuss transfer-function realization for multivariable holomorphic functions mapping the unit polydisk or the right polyhalfplane into the operator analogue of either the unit…
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…
Fixed point theorems for noncommutative functions
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi
We establish a fixed point theorem for mappings of square matrices of all sizes which respect the matrix sizes and direct sums of matrices. The conclusions are stronger if such a m…
Matrices with normal defect one
D. S. Kaliuzhnyi-Verbovetskyi, I. M. Spitkovsky, H. J. Woerdeman
A matrix has normal defect one if it is not normal, however can be embedded as a north-western block into a normal matrix of size . The latter is…