14 citations · 17 across the 4 of their papers we have counts for
4 papers
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…
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…
Sufficient and Necessary Conditions for Semidefinite Representability of Convex Hulls and Sets
J. William Helton, Jiawang Nie
A set $S\subseteq \re^n$ is called to be {\it Semidefinite (SDP)} representable if equals the projection of a set in higher dimensional space which is describable by some Linea…
Measures with zeros in the inverse of their moment matrix
J. William Helton, Jean B. Lasserre, Mihai Putinar
We investigate and discuss when the inverse of a multivariate truncated moment matrix of a measure has zeros in some prescribed entries. We describe precisely which pattern of…