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Iterated function systems, Ruelle operators, and invariant projective measures

Dorin Ervin Dutkay·Palle E. T. Jorgensen
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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 R_W acting on functions on X, and a corresponding class of R_W-harmonic functions. The properties of these functions determine the spectral theory of L^2(mu). For affine IFSs we establish orthogonal bases in L^2(mu). These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in R^d.

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Dorin Ervin Dutkay, Palle E. T. Jorgensen. 2005-01-06. Iterated function systems, Ruelle operators, and invariant projective measures. https://doi.org/10.1090/s0025-5718-06-01861-8

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