We revise the symmetries of the Zernike polynomials that determine the Lie algebra su(1, 1) ⊕ su(1, 1). We show how they induce discrete as
well as continuous bases that coexist in the framework of rigged Hilbert spaces. We also discuss some other interesting properties of Zernike
polynomials and Zernike functions. One of the areas of interest of Zernike functions has been their applications in optics. Here, we suggest
that operators on the spaces of Zernike functions may play a role in optical image processing.
