3 papers
math.OA2011
Noncommutative Plurisubharmonic Polynomials Part II: Local Assumptions
Jeremy M. Greene
We say that a symmetric noncommutative polynomial in the noncommutative free variables (x_1, x_2, ..., x_g) is noncommutative plurisubharmonic on a noncommutative open set if it ha…
math.OA2011
Noncommutative Plurisubharmonic Polynomials Part I: Global Assumptions
Jeremy M. Greene, J. William Helton, Victor Vinnikov
We consider symmetric polynomials, p, in the noncommutative free variables (x_1, x_2, ..., x_g). We define the noncommutative complex hessian of p and we call a noncommutative symm…
math.FA2009
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…