Zernike functions, rigged Hilbert spaces and potential applications
Mathematical Physics
2019-10-02 v2 math.MP
Optics
Abstract
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 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 interests 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.
Cite
@article{arxiv.1902.08017,
title = {Zernike functions, rigged Hilbert spaces and potential applications},
author = {Enrico Celeghini and Manuel Gadella and Mariano A del Olmo},
journal= {arXiv preprint arXiv:1902.08017},
year = {2019}
}
Comments
16 pages, 9 figures