Abstract
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.
Keywords
- Infinite products
- Cuntz algebras
- dynamical systems
- Julia sets
Dedicated to Lev Sakhnovich
Mathematics Subject Classification (2010). Primary: 40A20, 47B32; Secondary: 37F50.
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© 2015 Springer International Publishing Switzerland
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Alpay, D., Jorgensen, P., Lewkowicz, I., Martziano, I. (2015). Infinite Product Representations for Kernels and Iterations of Functions. In: Alpay, D., Kirstein, B. (eds) Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes. Operator Theory: Advances and Applications(), vol 244. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-10335-8_5
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DOI: https://doi.org/10.1007/978-3-319-10335-8_5
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-10334-1
Online ISBN: 978-3-319-10335-8
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