7 papers
Skew fields of non-commutative meromorphic functions affiliated to finite operator algebras
Méric L. Augat, Robert T. W. Martin, Maximilian Tornes +1
We embed skew fields of meromorphic functions in several non-commuting variables into the topological algebra of closed linear operators affiliated to a finite von Neumann alge…
A non-commutative de Branges-Rovnyak model for row contractions
Robert T. W. Martin, Jeet Sampat
We extend the de Branges-Rovnyak model for completely non-coisometric (CNC) linear contractions on a Hilbert space to the non-commutative multivariate setting of CNC row contractio…
Operator realizations about a matrix-centre
Ali Karoobi, Robert T. W. Martin, Maximilian Tornes
We develop a general theory of operator realizations, or ``linear representations" of analytic functions in several non-commuting variables about a matrix-centre. In particular we…
Rings of non-commutative functions and their fields of fractions
Méric L. Augat, Robert T. W. Martin, Eli Shamovich
Semi-free ideal rings, or semifirs, were introduced by Paul M. Cohn to study universal localizations in the non-commutative setting. We provide new examples of semifirs consisting…
Invariant Measures in Time-Delay Coordinates for Unique Dynamical System Identification
Jonah Botvinick-Greenhouse, Robert Martin, Yunan Yang
While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniq…
Operator realizations of non-commutative analytic functions
Méric L. Augat, Robert T. W. Martin, Eli Shamovich
A realization is a triple, , consisting of a tuple, , , of bounded linear operators on a separable, complex Hilbert space, $…
Quantum uncertainty and the spectra of symmetric operators
R. T. W. Martin, A. Kempf
In certain circumstances, the uncertainty, , of a quantum observable, , can be bounded from below by a finite overall constant , \emph{i.e.}, , for…