On domains of noncommutative rational functions

Jurij Volčič

doi:10.1016/j.laa.2016.11.031

On domains of noncommutative rational functions

Jurij Volčič

Research output: Contribution to journal › Article › peer-review

19 Scopus citations

Abstract

In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide.

Original language	English
Pages (from-to)	69-81
Number of pages	13
Journal	Linear Algebra and Its Applications
Volume	516
DOIs	https://doi.org/10.1016/j.laa.2016.11.031
State	Published - 1 Mar 2017
Externally published	Yes

Keywords

Extended domain
Free function theory
Minimal realization
Noncommutative rational function
Singularities

ASJC Scopus subject areas

Algebra and Number Theory
Numerical Analysis
Geometry and Topology
Discrete Mathematics and Combinatorics

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10.1016/j.laa.2016.11.031

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AB - In this paper the stable extended domain of a noncommutative rational function is introduced and it is shown that it can be completely described by a monic linear pencil from the minimal realization of the function. This result amends the singularities theorem of Kalyuzhnyi-Verbovetskyi and Vinnikov. Furthermore, for noncommutative rational functions which are regular at a scalar point it is proved that their domains and stable extended domains coincide.

KW - Extended domain

KW - Free function theory

KW - Minimal realization

KW - Noncommutative rational function

KW - Singularities

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ER -

On domains of noncommutative rational functions

Abstract

Keywords

ASJC Scopus subject areas

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