19 citations · 55 across the 7 of their papers we have counts for
9 papers
Norms of basic operators in vector valued model spaces and de Branges spaces
Kousik Dhara, Harry Dym
Let be either the open unit disc or the open upper half plane or the open right half plane. In this paper, we compute the norm of the basic operator $A_α=Π_ΘT_{b_α}|_{\mathca…
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…
Non-commutative polynomials with convex level slices
Harry Dym, J. William Helton, Scott McCullough
Let a and x denote tuples of (jointly) freely noncommuting variables. A square matrix valued polynomial p in these variables is naturally evaluated at a tuple (A,X) of symmetric ma…
Non-Commutative Representations of Families of k^2 Commutative Polynomials in 2k^2 Commuting Variables
Harry Dym, J. W. Helton, Caleb Meier
Given a collection P of k^2 commutative polynomials in 2k^2 commutative variables, the objective is to find a condensed representation of these polynomials in terms of a single non…
Non-commutative varieties with curvature having bounded signature
Harry Dym, J. William Helton, Scott McCullough
The signature(s) of the curvature of the zero set V of a free (non-commutative) polynomial is defined as the number of positive and negative eigenvalues of the non-commutative seco…
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…