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On monomial commutativity of operators satisfying commutation relations and periodic points for one-dimensional dynamical systems
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. Makerere University. (MAM)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (Mathematics and Applied Mathematics)ORCID iD: 0000-0003-4554-6528
2014 (English)In: 10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway ISBN: 978-0-7354-1276-7 Editor: Seenith Sivasundaram Volume number: 1637 Published: 10 december 2014 / [ed] Seenith Sivasundaram, American Institute of Physics (AIP), 2014, p. 1110-1119Conference paper, Published paper (Refereed)
Abstract [en]

T. Persson and S. D. Sivestrov investigated representations of operators satisfying the relation XX* = F(X*X) in connection with periodic points and orbits of the map F. In particular they derived commutativity conditions for two monomials in operators A and B on a Hilbert space satisfying the relation AB = BF(A). In this article we shall apply their results to special one-dimensional dynamical systems and and give an explicit description of the interplay between periodic orbits of one-dimensional piecewise polynomial maps and commutativity of monomials for special operators A and B. Furthermore we shall apply our results to derive conditions on β for the special case when F β is the β–shift dynamical system.

Place, publisher, year, edition, pages
American Institute of Physics (AIP), 2014. p. 1110-1119
National Category
Mathematics Algebra and Logic
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-27253DOI: 10.1063/1.4904686ISI: 000347812200129Scopus ID: 2-s2.0-85031861299OAI: oai:DiVA.org:mdh-27253DiVA, id: diva2:775308
Conference
10TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES: ICNPAA 2014 Conference date: 15–18 July 2014 Location: Narvik, Norway
Available from: 2014-12-31 Created: 2014-12-31 Last updated: 2018-04-17Bibliographically approved
In thesis
1. Dynamical Systems and Commutants in Non-Commutative Algebras
Open this publication in new window or tab >>Dynamical Systems and Commutants in Non-Commutative Algebras
2018 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This thesis work is about commutativity which is a very important topic in Mathematics, Physics, Engineering and many other fields. In Mathematics, it is well known that matrix multiplication (or composition of linear operators on a finite dimensional vector space) is not always commutative. Commuting matrices or more general linear or non-linear operators play an essential role in Mathematics and its applications in Physics and Engineering. Many important relations in Mathematics, Physics and Engineering are represented by operators satisfying a number of commutation relations. Such commutation relations are key in areas such as representation theory, dynamical systems, spectral theory, quantum mechanics, wavelet analysis and many others.

In Chapter 2 of this thesis we treat commutativity of monomials of operators satisfying certain commutation relations in relation to one-dimensional dynamical systems. We derive explicit conditions for commutativity of the said monomials in relation to the existence of periodic points of certain onedimensional dynamical systems.

In Chapter 3, we treat the crossed product algebra for the algebra of piecewise constant functions on given set and describe the commutant of this algebra of functions which happens to be the maximal commutative subalgebra of the crossed product containing this algebra.

In Chapters 4 and 5, we give a characterization of the commutant for the algebra of piecewise constant functions on the real line, by comparing commutants for a non-decreasing sequence of algebras.

In Chapter 6 we give a description of the centralizer of the coefficient algebra in the Ore extension of the algebra of functions on a countable set with finite support.

Place, publisher, year, edition, pages
Västerås: Mälardalen University, 2018. p. 140
Series
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 258
National Category
Natural Sciences
Research subject
Mathematics/Applied Mathematics
Identifiers
urn:nbn:se:mdh:diva-39000 (URN)978-91-7485-381-0 (ISBN)
Public defence
2018-05-29, Kappa, Mälardalens högskola, Västerås, 13:00 (English)
Opponent
Supervisors
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2018-04-17 Created: 2018-04-13 Last updated: 2018-05-07Bibliographically approved

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Publisher's full textScopushttp://scitation.aip.org/content/aip/proceeding/aipcp/1637

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Tumwesigye, AlexSilvestrov, Sergei

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