Infinite product representations for kernels and iterations of functions

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz, Itzik Martziano

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

12 Scopus citations


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.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Number of pages21
StatePublished - 1 Jan 2015

Publication series

NameOperator Theory: Advances and Applications
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878


  • Cuntz algebras
  • Dynamical systems
  • Infinite products
  • Julia sets

ASJC Scopus subject areas

  • Analysis


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