74 citations · 668 across the 48 of their papers we have counts for
5 papers · 1 filter
Non-Commutative Harmonic and Subharmonic Polynomials
J. William Helton, Daniel P. McAllaster, Joshua A. Hernandez
The paper introduces a notion of the Laplace operator of a polynomial p in noncommutative variables x=(x_1,...,x_g). The Laplacian Lap[p,h] of p is a polynomial in x and in a nonco…
Every free basic convex semi-algebraic set has an LMI representation
J. William Helton, Scott McCullough
The (matricial) solution set of a Linear Matrix Inequality (LMI) is a convex basic non-commutative semi-algebraic set. The main theorem of this paper is a converse, a result which…
Analytic mappings between noncommutative pencil balls
J. William Helton, Igor Klep, Scott McCullough
In this paper, we analyze problems involving matrix variables for which we use a noncommutative algebra setting. To be more specific, we use a class of functions (called NC analyti…
Sign patterns for chemical reaction networks
J. William Helton, Igor Klep, Vitaly Katsnelson
Most differential equations found in chemical reaction networks (CRNs) have the form , where lies in the nonnegative orthant, where is a real matrix (the…
Classification of All Noncommutative Polynomials Whose Hessian Has Negative Signature One and A Noncommutative Second Fundamental Form
Harry Dym, Jeremy M. Greene, J. William Helton +1
Every symmetric polynomial p(x)=p(x_1,...,x_g) (with real coefficients) in g noncommuting variables x_1, ..., x_g can be written as a sum and difference of squares of noncommutativ…