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We study infinite products of reproducing kernels with view to their use in dynamics (of iterated function systems), in harmonic analysis, and in stochastic processes. On the way, we construct a new family of representations of the Cuntz relations. Then, using these representations we associate a fixed filled Julia set with a Hilbert space. This is based on analysis and conformal geometry of a fixed rational mapping R in one complex variable, and its iterations.


This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Operator Theory: Advances and Applications, volume 244, in 2015 following peer review. The final publication is available at Springer via DOI: 10.1007/978-3-319-10335-8_5

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