Infinite Product Representations for Kernels and Iteration of Functions

Authors

Daniel Alpay, Chapman UniversityFollow
Palle Jorgensen, University of Iowa
Izchak Lewkowicz, Ben Gurion University of the Negev
Itzik Marziano, Ben Gurion University of the Negev

Document Type

Article

Publication Date

2015

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.

Comments

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Operator Theory: Advances and Applications, volume 244, in 2015 following peer review. The final publication is available at Springer via DOI: 10.1007/978-3-319-10335-8_5

Recommended Citation

D. Alpay, P. Jorgensen, I. Lewkowicz and I. Martziano. Infinite product representations for kernels and iteration of functions. Operator Theory: Advances and Applications, vol. 244 (2015), pp. 67-87.

Peer Reviewed

1

Copyright

Springer