6 papers
Non-commutative rational functions in the full Fock space
Michael T. Jury, Robert T. W. Martin, Eli Shamovich
A rational function belongs to the Hardy space, , of square-summable power series if and only if it is bounded in the complex unit disk. Any such rational function is necessar…
A de Branges-Beurling theorem for the full Fock space
Robert T. W. Martin, Eli Shamovich
We extend the de Branges-Beurling theorem characterizing the shift-invariant spaces boundedly contained in the Hardy space of square-summable power series to the full Fock space ov…
Blaschke-Singular-Outer factorization of free non-commutative functions
Michael T. Jury, Robert T. W. Martin, Eli Shamovich
By classical results of Herglotz and F. Riesz, any bounded analytic function in the complex unit disk has a unique inner-outer factorization. Here, a bounded analytic function is c…
Noncommutative Choquet simplices
Matthew Kennedy, Eli Shamovich
We introduce a notion of noncommutative Choquet simplex, or briefly an nc simplex, that generalizes the classical notion of a simplex. While every simplex is an nc simplex, there a…
Nevanlinna-Pick Families and Singular Rational Varieties
Kenneth R. Davidson, Eli Shamovich
The goal of this note is to apply ideas from commutative algebra (a.k.a. affine algebraic geometry) to the question of constrained Nevanlinna-Pick interpolation. More precisely, we…
How to count zeroes of polynomials on quadrature domains using the Bezout matrix
Eli Shamovich, Victor Vinnikov
Classically, the Bezout matrix or simply Bezoutian of two polynomials is used to locate the roots of the polynomial and, in particular, test for stability. In this paper, we develo…