mdh.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
On one-dimensional dynamical systems and commuting elements in non-commutative algebras
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0001-9658-1222
2016 (English)Licentiate thesis, monograph (Other academic)
Abstract [en]

This thesis work is about commutativity which is a very important topic in mathematics, physics, engineering and many other fields. Two processes are said to be commutative if the order of "operation" of these processes does not matter. A typical example of two processes in real life that are not commutative is the process of opening the door and the process of going through the door. In mathematics, it is well known that matrix multiplication is not always commutative. Commutating operators play an essential role in mathematics, physics engineering and many other fields. A typical example of the importance of commutativity comes from signal processing. Signals pass through filters (often called operators on a Hilbert space by mathematicians) and commutativity of two operators corresponds to having the same result even when filters are interchanged. Many important relations in mathematics, physics and engineering are represented by operators satisfying a number of commutation relations.

In chapter two of this thesis we treat commutativity of monomials of operatos 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 one-dimensional dynamical systems. In chapter three, we treat the crossed product algebra for the algebra of piecewise constant functions on given set, describe the commutant of this algebra of functions which happens to be the maximal commutative subalgebra of the crossed product containing this algebra. In chapter four, 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.

Place, publisher, year, edition, pages
Västerås: Mälardalen University , 2016.
Series
Mälardalen University Press Licentiate Theses, ISSN 1651-9256 ; 234
Keyword [en]
Commutativity, dynamical systems, commutant
National Category
Mathematics
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-31437ISBN: 978-91-7485-263-9 (print)OAI: oai:DiVA.org:mdh-31437DiVA: diva2:921142
Presentation
2016-05-26, Kappa, Mälardalen University, Västerås, 13:15 (English)
Opponent
Supervisors
Funder
Sida - Swedish International Development Cooperation Agency
Available from: 2016-04-20 Created: 2016-04-19 Last updated: 2016-12-27Bibliographically approved

Open Access in DiVA

fulltext(1119 kB)72 downloads
File information
File name FULLTEXT02.pdfFile size 1119 kBChecksum SHA-512
260b78821120690f143fc2813856392f9ca1e414e32ebf31921952433d33084fd22c426a5252fa871d3a5f4e89c4d9be9587acd5d7e5913240402479c3b609da
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Tumwesigye, Alex Behakanira
By organisation
Educational Sciences and Mathematics
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 72 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 526 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf