Home » Ruelle Operators: Functions Which Are Harmonic with Respect to a Transfer Operator by Palle E.T. Jorgensen
Ruelle Operators: Functions Which Are Harmonic with Respect to a Transfer Operator Palle E.T. Jorgensen

Ruelle Operators: Functions Which Are Harmonic with Respect to a Transfer Operator

Palle E.T. Jorgensen

Published August 1st 2001
ISBN : 9780821826881
Paperback
60 pages
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 About the Book 

Let $N/in/mathbb{N}$, $N/geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{/ast}$-algebra $/mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVUMoreLet $N/in/mathbb{N}$, $N/geq2$, be given. Motivated by wavelet analysis, this title considers a class of normal representations of the $C DEGREES{/ast}$-algebra $/mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU DEGREES{-1}=V DEGREES{N}$. The representations are in one-to-one correspondence with solutions $h/in L DEGREES{1}/left(/mathbb{T}/right)$, $h/geq0$, to $R/left(h/right)=h$ where $R$ is a certain transfer operator (positivity-preserving) which was studied previously by D. Ruelle. The representations of $/mathfrak{A}_{N}$ may also be viewed as representations of a certain (discrete) $N$-adic $ax+b$ group which was considered recently