Iterated function systems, Ruelle operators, and invariant projective measures
Dorin Ervin Dutkay, Palle E. T. Jorgensen
Abstract
We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator RW acting on functions on X, and a corresponding class of RW-harmonic functions. The properties of these functions determine the spectral theory of L2(mu). For affine IFSs we establish orthogonal bases in L2(mu). These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in Rd.
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