Implicit/inverse function theorems for free noncommutative functions
Gulnara Abduvalieva, Dmitry S. Kaliuzhnyi-Verbovetskyi
TL;DR
This paper establishes implicit and inverse function theorems for free noncommutative functions, enabling analysis of solutions to noncommutative ODEs and extremal problems with constraints.
Contribution
It introduces new theorems for free noncommutative functions over operator spaces and nilpotent matrices, expanding tools for noncommutative analysis.
Findings
Proved implicit and inverse function theorems for free noncommutative functions.
Applied the theorems to study solution dependence in noncommutative ODEs.
Addressed extremal problems with noncommutative constraints.
Abstract
We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial value problem for ODEs in noncommutative spaces on the initial data and to extremal problems with noncommutative constraints.
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