Palle E.T. Jorgensen
Ruelle operators: Functions which are harmonic with respect to a transfer operator
(338K, LaTeX2e memo-l class; 64 pages, 4 figures with 7 EPS graphics)

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 one-to-one correspondence with solutions h \in 
L^1(T), h \geq 0, to R(h)=h where 
R is a certain transfer operator (positivity-preserving) which was studied 
previously by D. Ruelle. The representations of 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.