Commuting Operators for Representations of Commutation Relations Defined by Dynamical Systems

Summary, in English

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.

• Författare: Tomas Persson; Sergei D. Silvestrov
• Avdelning/ar: Matematik LTH; Dynamical systems
• Publiceringsår: 2012
• Språk: Engelska
• Sidor: 1126-1165
• Publikation/Tidskrift/Serie: Numerical Functional Analysis and Optimization
• Volym: 33
• Issue: 7-9
• Länkar: http://dx.doi.org/10.1080/01630563.2012.682143
• Dokumenttyp: Artikel i tidskrift
• Förlag: Taylor & Francis
• Ämne: Mathematics
• Nyckelord: Commutation relations; Commuting elements; Dynamical systems; Periodic; points; Representations; Spectral measure
• Status: Published
• Forskningsgrupp: Dynamical systems
• ISBN/ISSN/Övrigt: ISSN: 1532-2467