12 citations · 34 across the 6 of their papers we have counts for
7 papers
On trace-convex noncommutative polynomials
Igor Klep, Scott A. McCullough, Christopher S. Nelson
To each real continuous function f there is an associated trace function on real symmetric matrices Tr f. The classical Klein lemma states that f is convex if and only if Tr f is c…
Noncommutative polynomials nonnegative on a variety intersect a convex set
J. William Helton, Igor Klep, Christopher S. Nelson
By a result of Helton and McCullough, open bounded convex free semialgebraic sets are exactly open (matricial) solution sets D_L of a linear matrix inequality (LMI) L(X)>0. This pa…
A Real Nullstellensatz for Matrices of Non-Commutative Polynomials
Christopher S. Nelson
This article extends the classical Real Nullstellensatz to matrices of polynomials in a free -algebra $\RR\axs$ with . This result is a generalization o…
Real Nullstellensatze and *-ideals in *-algebras
Jakob Cimpric, J. William Helton, Scott McCullough +1
Let F denote either the real or complex field. An ideal I in the free *-algebra F<x,x*> in g freely noncommuting variables and their formal adjoints is a *-ideal if I = I*. When a…
On real one-sided ideals in a free algebra
Jakob Cimprič, J. William Helton, Igor Klep +2
In classical and real algebraic geometry there are several notions of the radical of an ideal I. There is the vanishing radical defined as the set of all real polynomials vanishing…
Noncommutative Harmonic and Subharmonic Polynomials and other Noncommutative Partial Differential Equations
Christopher Nelson
Solutions to Laplace's equation are called harmonic functions. Harmonic functions arise in many applications, such as physics and the theory of stochastic processes. Of interest cl…