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Ruelle Operators
Functions which Are Harmonic with Respect to a Transfer Operator
PDF
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ISBN-13:
9781470403133
Einband:
PDF
Seiten:
60
Autor:
Palle E. T Jorgensen
eBook Typ:
PDF
eBook Format:
PDF
Kopierschutz:
Adobe DRM [Hard-DRM]
Sprache:
Deutsch
Beschreibung:
Let $Ninmathbb{N}$, $Ngeq2$, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $C^{ast}$-algebra $mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU^{-1}=V^{N}$. The representations are in one-to-one correspondence with solutions $hin L^{1}left(mathbb{T}ight)$, $hgeq0$, to $Rleft(hight)=h$ 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 by J.-B. Bost and A. Connes.
Let $Ninmathbb{N}$, $Ngeq2$, be given. Motivated by wavelet analysis, we consider a class of normal representations of the $C^{ast}$-algebra $mathfrak{A}_{N}$ on two unitary generators $U$, $V$ subject to the relation $UVU^{-1}=V^{N}$. The representations are in one-to-one correspondence with solutions $hin L^{1}left(mathbb{T}ight)$, $hgeq0$, to $Rleft(hight)=h$ 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 by J.-B. Bost and A. Connes.