Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems
(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.
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/3070054
- author
- Persson, Tomas LU and Silvestrov, Sergei D.
- organization
- publishing date
- 2012
- 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
- 2016-04-01 10:32:42
- date last changed
- 2022-01-26 00:17:00
@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}}, keywords = {{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}}, doi = {{10.1080/01630563.2012.682143}}, volume = {{33}}, year = {{2012}}, }