28 citations · 197 across the 30 of their papers we have counts for
7 papers · 1 filter
Addendum to "Factoring non-negative operator valued trigonometric polynomials in two variables"
Michael A. Dritschel, Igor Klep, Scott McCullough +1
Factorization for positive semidefinite matrix-valued polynomials over a nonsingular compact affine real surface is established. Corollaries include Fejér-Riesz factorization for b…
Linear matrix pencils and noncommutative convexity
Jurij Volčič
Hermitian linear matrix pencils are ubiquitous in control theory, operator systems, semidefinite optimization, and real algebraic geometry. This survey reviews the fundamental feat…
Sums of squares certificates for polynomial moment inequalities
Igor Klep, Victor Magron, Jurij Volčič
This paper introduces and develops the algebraic framework of moment polynomials, which are polynomial expressions in commuting variables and their formal mixed moments. Their posi…
State polynomials: positivity, optimization and nonlinear Bell inequalities
Igor Klep, Victor Magron, Jurij Volčič +1
This paper introduces state polynomials, i.e., polynomials in noncommuting variables and formal states of their products. A state analog of Artin's solution to Hilbert's 17th probl…
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…
Noncommutative polynomials describing convex sets
J. W. Helton, I. Klep, S. McCullough +1
The free closed semialgebraic set determined by a hermitian noncommutative polynomial is the closure of the connected component of containing…
Bianalytic free maps between spectrahedra and spectraballs
J. William Helton, Igor Klep, Scott McCullough +1
Linear matrix inequalities (LMIs) are ubiquitous in real algebraic geometry, semidefinite programming, control theory and signal processing. LMIs with (dimension free) matrix unkno…