00-446 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) 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 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.

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