Foundations of Free Noncommutative Function Theory

2012/12/27 by Dmitry S. Kaliuzhnyi-Verbovetskyi, Victor Vinnikov, Kaliuzhnyi-Verbovetskyi, Dmitry S. +1 · 6 citations
Computer Science · Mathematics · #17A50 #40A05 #4602 #46L52 #46L54 #47A60 #47L25 #Computability, Logic, AI Algorithms #FOS: Mathematics #Mathematical and Theoretical Analysis #Operator Algebras (math.OA) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1212.6345

openalex publication_date 2012/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The goal of this work is to develop, in a systematic way and in a full natural generality, the foundations of a theory of functions of (free) noncommuting variables.

Cited by

• Fejér--Riesz factorization for positive noncommutative trigonometric polynomials
• Positive operator-valued noncommutative polynomials are squares
• Zeros of Holomorphic Functions in Commuting and Non-commuting Variables as Spectral Data
• Rings of non-commutative functions and their fields of fractions
• Operator realizations about a matrix-centre
• A Noncommutative Szegő-Type Theorem on the Row-Ball

Related

• Integrability of Free Noncommutative Functions
• Noncommutative Vieta Theorem and Symmetric Functions
• Implicit/inverse function theorems for free noncommutative functions
• Noncommutative identities
• Free holomorphic functions and operator model theory