 00446 Palle E.T. Jorgensen
 Ruelle operators: Functions which are harmonic with respect to a transfer operator
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Nov 9, 00

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Abstract. Let a natural number N greater than or equal to 2 be given. Motivated by wavelet analysis, we
consider a class of normal representations of the C*algebra
A_N on two unitary generators U, V subject to the relation
UVU^{1}=V^N.
The representations are in onetoone correspondence with solutions h \in
L^1(T), h \geq 0, to R(h)=h where
R is a certain transfer operator (positivitypreserving) which was studied
previously by D. Ruelle. The representations of A_N may also be
viewed as representations of a certain (discrete) Nadic ax+b group which
was considered recently by J.B. Bost and A. Connes.
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