2D-Zernike polynomials and coherent state quantization of the unit disc

K. Thirulogasanthar; Nasser Saad; G. Honnouvo

2D-Zernike polynomials and coherent state quantization of the unit disc

Mathematical Physics 2015-01-08 v3 math.MP

Authors: K. Thirulogasanthar , Nasser Saad , G. Honnouvo

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.

Keywords

2d-zernike polynomials coherent state quantization reproducing kernel hilbert spaces berezin transform unit disc summation formulas

Cite

@article{arxiv.1303.5483,
  title  = {2D-Zernike polynomials and coherent state quantization of the unit disc},
  author = {K. Thirulogasanthar and Nasser Saad and G. Honnouvo},
  journal= {arXiv preprint arXiv:1303.5483},
  year   = {2015}
}

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15 pages In Mathematical Physics, Analysis and Geometry, Jan. 7, 2015

2D-Zernike polynomials and coherent state quantization of the unit disc

Abstract

Keywords

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