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Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems

Persson, Tomas LU and Silvestrov, Sergei D. (2012) In Numerical Functional Analysis and Optimization 33(7-9). p.1126-1165
Abstract
In this article, using orbits of the dynamical system generated by the function F, operator representations of commutation relations XX* = F (X* X) and AB = BF (A) are studied and used to investigate commuting operators expressed using polynomials in A and B. Various conditions on the function F, defining the commutation relations, are derived for monomials and polynomials in operators A and B to commute. These conditions are further studied for dynamical systems generated by affine and q-deformed power functions, and for the beta-shift dynamical system.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Commutation relations, Commuting elements, Dynamical systems, Periodic, points, Representations, Spectral measure
in
Numerical Functional Analysis and Optimization
volume
33
issue
7-9
pages
1126 - 1165
publisher
Taylor & Francis
external identifiers
  • wos:000307080400020
  • scopus:84864719377
ISSN
1532-2467
DOI
10.1080/01630563.2012.682143
language
English
LU publication?
yes
id
ba360414-6b76-497b-9ac3-71ce7799f58d (old id 3070054)
date added to LUP
2012-09-26 15:43:32
date last changed
2017-03-14 13:40:53
@article{ba360414-6b76-497b-9ac3-71ce7799f58d,
  abstract     = {In this article, using orbits of the dynamical system generated by the function F, operator representations of commutation relations XX* = F (X* X) and AB = BF (A) are studied and used to investigate commuting operators expressed using polynomials in A and B. Various conditions on the function F, defining the commutation relations, are derived for monomials and polynomials in operators A and B to commute. These conditions are further studied for dynamical systems generated by affine and q-deformed power functions, and for the beta-shift dynamical system.},
  author       = {Persson, Tomas and Silvestrov, Sergei D.},
  issn         = {1532-2467},
  keyword      = {Commutation relations,Commuting elements,Dynamical systems,Periodic,points,Representations,Spectral measure},
  language     = {eng},
  number       = {7-9},
  pages        = {1126--1165},
  publisher    = {Taylor & Francis},
  series       = {Numerical Functional Analysis and Optimization},
  title        = {Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems},
  url          = {http://dx.doi.org/10.1080/01630563.2012.682143},
  volume       = {33},
  year         = {2012},
}