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2D-Zernike Polynomials and Coherent State Quantization of the Unit Disc

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Abstract

Using the orthonormality of the 2D-Zernike polynomials, reproducing kernels, reproducing kernel Hilbert spaces, and ensuring coherent states attained. With the aid of the so-obtained coherent states, the complex unit disc is quantized. Associated upper symbols, lower symbols and related generalized Berezin transforms also obtained. A number of necessary summation formulas for the 2D-Zernike polynomials proved.

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Authors and Affiliations

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

    K. Thirulogasanthar

  2. Department of mathematics and Statistics, University of Prince Edward Island, 550 University avenue, Charlottetown, UPEI, C1A 4P3, Canada

    Nasser Saad

  3. Department of Mathematics and Statistics, McGill University, 05 Sherbrooke Street w., Montreal, Quebec, H3A 2K6, Canada

    G. Honnouvo

Authors
  1. K. Thirulogasanthar
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  2. Nasser Saad
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  3. G. Honnouvo
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Corresponding author

Correspondence to Nasser Saad.

Additional information

The research of one of the authors (NS) was supported by the Natural Science and Engineering Research Council of Canada (NSERC)

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Thirulogasanthar, K., Saad, N. & Honnouvo, G. 2D-Zernike Polynomials and Coherent State Quantization of the Unit Disc. Math Phys Anal Geom 18, 13 (2015). https://doi.org/10.1007/s11040-015-9172-y

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  • DOI: https://doi.org/10.1007/s11040-015-9172-y

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