28 citations · 197 across the 30 of their papers we have counts for
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Hereditary NC Polynomials & Positivity Domains
Abdellah Islam, Jurij Volčič, Hugo J. Woerdeman
Noncommutative polynomials, elements of the free algebra generated by several noncommuting variables , are of importance in noncommutative algebra, fre…
Global structure behind pointwise equivalences of noncommutative polynomials
Eli Shamovich, Jurij Volčič
This paper investigates the interplay between local and global equivalences on noncommutative polynomials, the elements of the free algebra. When the latter are viewed as functions…
Dimension-free matricial Nullstellensätze for noncommutative polynomials
Jurij Volčič
Hilbert's Nullstellensatz is one of the most fundamental correspondences between algebra and geometry, and has inspired a plethora of noncommutative analogs. In last two decades, t…
Matrix evaluations of noncommutative rational functions and Waring problems
Matej Brešar, Jurij Volčič
Let be a nonconstant noncommutative rational function in variables over an algebraically closed field of characteristic 0. We show that for large enough, there exis…
Ranks of linear matrix pencils separate simultaneous similarity orbits
Harm Derksen, Igor Klep, Visu Makam +1
This paper solves the two-sided version and provides a counterexample to the general version of the 2003 conjecture by Hadwin and Larson. Consider evaluations of linear matrix penc…
Hilbert's 17th problem in free skew fields
Jurij Volčič
This paper solves the rational noncommutative analog of Hilbert's 17th problem: if a noncommutative rational function is positive semidefinite on all tuples of hermitian matrices i…
Positive univariate trace polynomials
Igor Klep, James Eldred Pascoe, Jurij Volčič
A univariate trace polynomial is a polynomial in a variable x and formal trace symbols Tr(x^j). Such an expression can be naturally evaluated on matrices, where the trace symbols a…
Noncommutative rational functions invariant under the action of a finite solvable group
Igor Klep, James Eldred Pascoe, Gregor Podlogar +1
This paper describes the structure of invariant skew fields for linear actions of finite solvable groups on free skew fields in generators. These invariant skew fields are alwa…
Free Bertini's theorem and applications
Jurij Volčič
The simplest version of Bertini's irreducibility theorem states that the generic fiber of a non-composite polynomial function is an irreducible hypersurface. The main result of thi…
Factorization of noncommutative polynomials and Nullstellensätze for the free algebra
J. William Helton, Igor Klep, Jurij Volčič
This article gives a class of Nullstellensätze for noncommutative polynomials. The singularity set of a noncommutative polynomial is , where $…
Local theory of free noncommutative functions: germs, meromorphic functions and Hermite interpolation
Igor Klep, Victor Vinnikov, Jurij Volčič
Free analysis is a quantization of the usual function theory much like operator space theory is a quantization of classical functional analysis. Basic objects of free analysis are…
Stable noncommutative polynomials and their determinantal representations
Jurij Volčič
A noncommutative polynomial is stable if it is nonsingular on all tuples of matrices whose imaginary parts are positive definite. In this paper a characterization of stable polynom…
Geometry of free loci and factorization of noncommutative polynomials
J. William Helton, Igor Klep, Jurij Volčič
The free singularity locus of a noncommutative polynomial f is defined to be the sequence of hypersurfaces. The main theorem of this article s…
Skolem-Noether algebras
Matej Brešar, Christoph Hanselka, Igor Klep +1
An algebra is called a Skolem-Noether algebra (SN algebra for short) if for every central simple algebra , every homomorphism extends to an inner automorph…
Positive trace polynomials and the universal Procesi-Schacher conjecture
Igor Klep, Špela Špenko, Jurij Volčič
Positivstellensatz is a fundamental result in real algebraic geometry providing algebraic certificates for positivity of polynomials on semialgebraic sets. In this article Positivs…
On domains of noncommutative rational functions
Jurij Volčič
In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the m…
Regular and positive noncommutative rational functions
Igor Klep, James Eldred Pascoe, Jurij Volčič
Call a noncommutative rational function regular if it has no singularities, i.e., is defined for all tuples of self-adjoint matrices . In this article regular noncomm…
Free loci of matrix pencils and domains of noncommutative rational functions
Igor Klep, Jurij Volčič
Consider a monic linear pencil whose coefficients are matrices. It is naturally evaluated at -tuples of matrices usi…
Multipartite rational functions
Igor Klep, Victor Vinnikov, Jurij Volčič
Consider a tensor product of free algebras over a field , the so-called multipartite free algebra . It is…
Matrix coefficient realization theory of noncommutative rational functions
Jurij Volčič
Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressi…
Null- and Positivstellensätze for rationally resolvable ideals
Igor Klep, Victor Vinnikov, Jurij Volčič
Hilbert's Nullstellensatz characterizes polynomials that vanish on the vanishing set of an ideal in C[x]. In the free algebra C<X> the vanishing set of a two-sided ideal I is defin…