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Mathematical Physics, Analysis and Geometry

, Volume 10, Issue 4, pp 297–312 | Cite as

Reproducing Kernels and Coherent States on Julia Sets

  • K. ThirulogasantharEmail author
  • A. Krzyżak
  • G. Honnouvo
Article
  • 69 Downloads

Abstract

We construct classes of coherent states on domains arising from dynamical systems. An orthonormal family of vectors associated to the generating transformation of a Julia set is found as a family of square integrable vectors, and, thereby, reproducing kernels and reproducing kernel Hilbert spaces are associated to Julia sets. We also present analogous results on domains arising from iterated function systems.

Keywords

Coherent states Reproducing kernel Julia sets IFS Attractor 

Mathematics Subject Classifications (2000)

Primary 81R30 46E22 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Department of Computer Science and Software EngineeringConcordia UniversityMontrealCanada
  2. 2.Department of Mathematics and StatisticsConcordia UniversityMontrealCanada

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