ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: Primary 46L60, 47D25, 42A16, 43A65; Secondary 46L45, 42A65, 41A15 Jorgensen, Palle E. T., The University of Iowa Ruelle operators: Functions which are harmonic with respect to a transfer operator Let N ∈ ℕ, N ≥ 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

UV U^{−1} = V^{N}.

The representations are in one-to-one correspondence with solutions h ∈ L^{1} (𝕋), h ≥ 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) N-adic ax + b group which was considered recently by J. -B. Bost and A. Connes.