38 citations · 43 across the 15 of their papers we have counts for
18 papers
Non-existence of co-spectral simple connected graphs with small number of edges
O. Boyko, D. Kaliuzhnyi-Verbovetskyi, V. Pivovarchik
We prove that if the number of edges does not exceed 7 then the asymptotics of eigenvalues of the Dirichlet problem uniquely determine the shape of the graph.
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…
Sparse Monte Carlo method for nonlocal diffusion problems
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
A class of evolution equations with nonlocal diffusion is considered in this work. These are integro-differential equations arising as models of propagation phenomena in continuum…
The mean field equation for the Kuramoto model on graph sequences with non-Lipschitz limit
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
The Kuramoto model (KM) of coupled phase oscillators on graphs provides the most influential framework for studying collective dynamics and synchronization. It exhibits a rich repe…
The semilinear heat equation on sparse random graphs
Dmitry Kaliuzhnyi-Verbovetskyi, Georgi S. Medvedev
Using the theory of -graphons (Borgs et al, 2014), we derive and rigorously justify the continuum limit for systems of differential equations on sparse random graphs. Specific…
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…
Implicit/inverse function theorems for free noncommutative functions
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these re…
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…
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…
Foundations of Free Noncommutative Function Theory
Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov
The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.
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…
Noncommutative rational functions, their difference-differential calculus and realizations
Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We sur…
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…