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.
CITATION STYLE
Alpay, D., Jorgensen, P., Lewkowicz, I., & Martziano, I. (2015). Infinite product representations for kernels and iterations of functions. In Operator Theory: Advances and Applications (Vol. 244, pp. 67–87). Springer International Publishing. https://doi.org/10.1007/978-3-319-10335-8_5
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