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

Using the orthonormality of the 2D-Zernike polynomials reproducing kernels, reproducing kernel Hilbert spaces and ensuing coherent states are 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 are also obtained. Along the way, necessary summation formulas for the 2D-Zernike polynomials are proved.