Infinite product representations for kernels and iterations of functions

2013/01/20 by D. Alpay, Alpay, D., P. Jorgensen +5
Economics, Econometrics and Finance · Mathematics · #37F50 #40A20 #47B32 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical Dynamics and Fractals #Stochastic processes and financial applications #math.FA #msc:37F50 #msc:40A20 #msc:47B32

paper · pdf · doi:10.48550/arxiv.1301.4626

arxiv created 2013/01/20 · openalex publication_date 2013/01/20 · arxiv updated 2013/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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