116 citations · 1.1k across the 72 of their papers we have counts for
6 papers · 1 filter
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…
Sparse Noncommutative Polynomial Optimization
Igor Klep, Victor Magron, Janez Povh
This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity in the input data. A converging hierarchy of semidefinite relaxati…
Noncommutative partial convexity via -convexity
Michael Jury, Igor Klep, Mark E. Mancuso +2
Motivated by classical notions of partial convexity, biconvexity, and bilinear matrix inequalities, we investigate the theory of free sets that are defined by (low degree) noncommu…
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…
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…