3 citations · 3 across the 1 of their papers we have counts for
8 papers
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…
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…
Plurisubharmonic Noncommutative Rational Functions
Harry Dym, J. William Helton, Igor Klep +2
A noncommutative (nc) function in is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neig…
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…