2D-Zernike polynomials and coherent state quantization of the unit disc
arXiv:1303.5483
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.
15 pages In Mathematical Physics, Analysis and Geometry, Jan. 7, 2015