Search
Search Results
-
A Brief Introduction to Noncommutative Function Theory
This survey provides a very brief introduction to the notion of a noncommutative function, with a particular emphasis on those parts of the theory...
-
Operator Theory on Noncommutative Polydomains, I
The goal of this paper is to study the noncommutative polydomains and their universal operator models generated by admissible k-tuples of formal...
-
The Emergence of Noncommutative Potential Theory
We review origins and developments of Noncommutative Potential Theory as underpinned by the notion of energy form. Recent and new applications are...
-
Noncommutative analysis of Hermite expansions
This paper is devoted to the study of semi-commutative harmonic analysis associated with Hermite semigroups. In the first part, we establish the...
-
Operator Theory on Noncommutative Polydomains, I
The goal of this paper is to study the noncommutative polydomains and their universal operator models generated by admissible k -tuples of formal...
-
Multivariable Beurling–Lax representations: the commutative and free noncommutative settings
The original theorem of Beurling asserts that any invariant subspace for the shift operator (multiplication by the coordinate function
... -
Nonlinear partial differential equations on noncommutative Euclidean spaces
Noncommutative Euclidean spaces—otherwise known as Moyal spaces or quantum Euclidean spaces—are a standard example of a non-compact noncommutative...
-
Function Theory from Tensor Algebras
We survey connections between our work on tensor algebras over \(C^*\)...
-
Noncommutative Geometry of Random Surfaces
AbstractWe associate a noncommutative curve to a periodic, bipartite, planar dimer model with polygonal boundary. It determines the inverse...
-
Convergence for noncommutative rational functions evaluated in random matrices
One of the main applications of free probability is to show that for appropriately chosen independent copies of d random matrix models, any...
-
Noncommutative Gröbner Bases and Ext Groups
We consider a theory of noncommutative Gröbner bases on decreasingly filtered algebras whose associated graded algebras are commutative. We transfer...
-
The Noncommutative Space of Penrose Tilings
In this chapter, we study the space parameterizing inequivalent Penrose tilings from the point of view of Noncommutative Geometry. This chapter is a...
-
L-functions of noncommutative tori
We introduce an analog of the L -function for noncommutative tori. It is proved that such a function coincides with the Hasse–Weil L -function of an...
-
Characteristic functions and functional models on noncommutative varieties
In this paper we develop a Sz.-Nagy-Foiaş type theory of characteristic functions and functional models on noncommutative domains and varieties in
... -
Globally trace-positive noncommutative polynomials and the unbounded tracial moment problem
A noncommutative (nc ) polynomial is called (globally) trace-positive if its evaluation at any tuple of operators in a tracial von Neumann algebra...
-
Weighted Hardy Spaces Over the Unit Ball: The Freely Noncommutative and Commutative Settings
It is known that backward-shift-invariant subspaces of the Hardy space...
-
A Theory of Singular Values for Finite Free Probability
We introduce a finite version of free probability for rectangular matrices that amounts to operations on singular values of polynomials. This study...