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Reproducing Kernels and Coherent States on Julia Sets

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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.

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Authors and Affiliations

  1. Department of Computer Science and Software Engineering, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, Canada, H3G 1M8

    K. Thirulogasanthar & A. Krzyżak

  2. Department of Mathematics and Statistics, Concordia University, 1455 De Maisonneuve Blvd. West, Montreal, Quebec, Canada, H3G 1M8

    G. Honnouvo

Authors
  1. K. Thirulogasanthar
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  2. A. Krzyżak
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  3. G. Honnouvo
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Corresponding author

Correspondence to K. Thirulogasanthar.

Additional information

The research of the first two authors was supported by Natural Sciences and Engineering Research Council of Canada.

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Thirulogasanthar, K., Krzyżak, A. & Honnouvo, G. Reproducing Kernels and Coherent States on Julia Sets. Math Phys Anal Geom 10, 297–312 (2007). https://doi.org/10.1007/s11040-008-9034-y

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  • DOI: https://doi.org/10.1007/s11040-008-9034-y

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