12 citations · 21 across the 9 of their papers we have counts for
11 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…
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…
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, $…
An Optimal Approximation Problem For Free Polynomials
Palak Arora, Meric Augat, Michael Jury +1
Motivated by recent work on optimal approximation by polynomials in the unit disk, we consider the following noncommutative approximation problem: for a polynomial in freel…
Operator NC functions
Meric Augat, John E. McCarthy
We establish a theory of NC functions on a class of von Neumann algebras with a particular direct sum property, e.g. . In contrast to the theory's origins, we do no…
Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications
Meric Augat, Michael T. Jury, James Eldred Pascoe
We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation proble…
Free potential functions
Meric L. Augat
This article establishes free versions of two classical theorems: derivatives are curl-free and every curl-free vector field (on a simply connected domain) is a derivative. We show…
The free Grothendieck theorem
Meric L. Augat
The main result of this article establishes the free analog of Grothendieck's Theorem on bijective polynomial mappings of . Namely, we show if is a polynomial map…
Free bianalytic maps between spectrahedra and spectraballs in a generic setting
Meric Augat, J. William Helton, Igor Klep +1
Given a tuple of matrices, the collection of those tuples of matrices (of the same size) such that $\| \sum E_j\otimes X_j\|\le…
Bianalytic Maps Between Free Spectrahedra
Meric Augat, J. William Helton, Igor Klep +1
Linear matrix inequalities (LMIs) play a role in many areas of applications and the set of solutions to one is called…
Compact Sets in the Free Topology
Meric Augat, Sriram Balasubramanian, Scott McCullough
Subsets of the set of -tuples of matrices that are closed with respect to direct sums and compact in the free topology are characterized. They are, in a dilation theoretic sense…