Infinite Product Representations for Kernels and Iterations of Functions

Daniel Alpay; Palle Jorgensen; Izchak Lewkowicz; Itzik Martziano

doi:10.1007/978-3-319-10335-8_5

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Book chapter

Infinite Product Representations for Kernels and Iterations of Functions

Daniel Alpay, Palle Jorgensen, Izchak Lewkowicz and Itzik Martziano

Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes, pp.67-87

Operator Theory: Advances and Applications, Springer International Publishing

2015

DOI: 10.1007/978-3-319-10335-8_5

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https://digitalcommons.chapman.edu/cgi/viewcontent.cgi?article=1436&context=scs_articlesView

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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.

Cuntz algebras

dynamical systems

Infinite products

Julia sets

Details

Title: Subtitle: Infinite Product Representations for Kernels and Iterations of Functions
Creators: Daniel Alpay - Ben-Gurion University of the Negev
Palle Jorgensen - Department of Mathematics 14 MLH, The University of Iowa, Iowa City, USA
Izchak Lewkowicz - Ben-Gurion University of the Negev
Itzik Martziano - Ben-Gurion University of the Negev
Resource Type: Book chapter
Publication Details: Recent Advances in Inverse Scattering, Schur Analysis and Stochastic Processes, pp.67-87
Series: Operator Theory: Advances and Applications
DOI: 10.1007/978-3-319-10335-8_5
eISSN: 2296-4878
ISSN: 0255-0156
Publisher: Springer International Publishing; Cham
Language: English
Date published: 2015
Academic Unit: Mathematics
Record Identifier: 9984241153302771

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