Related papers: Foundations of Free Noncommutative Function Theory
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
The foundations of non-linear quantum mechanics are based on six postulates and five propositions. On a first quantised level, these approaches are built on non-linear differential operators, non-linear eigenvalue equations, and the notion…
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…
Since the subject of noncommutative geometry is now entering maturity, we felt there is need for presentation of the material at an undergraduate course level. Our review is a zero order approximation to this project. Thus, the present…
Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
In this paper we develop a theory of free holomorphic functions on noncommutative Reinhardt domains generated by positive regular free holomorphic functions in n noncommuting variables. We show that the free biholomorphic classification of…
We develop a functional calculus for $d$-tuples of non-commuting elements in a Banach algebra. The functions we apply are free analytic functions, that is nc functions that are bounded on certain polynomial polyhedra.
We present the basic elements of a generalization of symmetric function theory involving functions of commuting and anticommuting (Grassmannian) variables. These new functions, called symmetric functions in superspace, are invariant under…
This is an expository article on the noncommutative singularity theory of power series in noncommuting variables, its motivation from deformation theory, and its applications to contractibility of curves and the classification of smooth…
The object of this lecture is to propose a series of conjectures and problems in different fields of analysis. They have been formulated with the aim of introducing some innovative methods in the study of classical topics, as open mappings,…
The aim of this paper is to give the text of a recent introduction to nonlinear generalized functions exposed in my talk in the congress gf2011, which was asked by several participants. Three representative topics were presented: two…
This is a continuation of the paper entitled "Free biholomorphic functions and operator model theory", in our attempt to transfer the free analogue of Nagy-Foias theory from the unit ball $[B(\cH)^n]_1$ to other noncommutative domains and…
Field theory and gauge theory on noncommutative spaces have been established as their own areas of research in recent years. The hope prevails that a noncommutative gauge theory will deliver testable experimental predictions and will thus…
The main aim of this work is to present the interpretation of the Ising type models as a kind of field theory in the framework of noncommutative geometry. We present the method and construct sample models of field theory on discrete spaces…
This talk is organized as follows: First we explain some basic concepts in non-commutative probability theory in the frame of operator algebras. In Section 2, we discuss related topics in von Neumann algebras. Sections 3 and 4 contain some…
We review some of the basic mathematical results about density functional theory.
This paper develops a free energy theory from physics including the variational principles for automata and languages and also provides algorithms to compute the energy as well as efficient algorithms for estimating the nondeterminism in a…
A novel class of derivative-free optimization algorithms is developed. The main idea is to utilize certain non-commutative maps in order to approximate the gradient of the objective function. Convergence properties of the novel algorithms…
The focus of this paper is providing a description of the spaces of counting functions on free monoids and groups and of the Brooks space. These results have been obtained in an earlier publication, however we propose an alternative,…
Noncommutative rational functions, i.e., elements of the universal skew field of fractions of a free algebra, can be defined through evaluations of noncommutative rational expressions on tuples of matrices. This interpretation extends their…