On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

Shlomi Steinberg; Ömer Eğecioğlu; Ling-Qi Yan

doi:10.15672/hujms.1114405

Abstract

The Hermite-Gauss basis functions have been extensively employed in classical and quantum optics due to their convenient analytic properties. A class of multivariate Hermite-Gauss functions—the anisotropic Hermite-Gauss functions—arise by endowing the standard univariate Hermite-Gauss functions with a positive definite quadratic form. These functions admit useful applications in optics, signal analysis and probability theory, however they have received little attention in literature. In this paper, we examine the properties of these functions, with an emphasis on applications in computational optics.

Cite this work

Shlomi Steinberg, Ömer Eğecioğlu, Ling-Qi Yan. 2024. On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions. Hacettepe Journal of Mathematics and Statistics, 53(2), 405–416. https://doi.org/10.15672/hujms.1114405

View BibTeX

@article{Steinberg_AHG_Functions_2024,
  author = {Shlomi Steinberg and Ömer Eğecioğlu and Ling-Qi Yan},
  doi = {10.15672/hujms.1114405},
  journal = {Hacettepe Journal of Mathematics and Statistics},
  keywords = {hermite functions, orthogonal basis, computational optics, linear canonical transform, fourier transform, wigner-ville distribution, eigenfunctions},
  number = {2},
  pages = {405--416},
  publisher = {Hacettepe University},
  title = {{On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions}},
  url = {https://ssteinberg.xyz/2023/05/23/properties_of_AHG_functions/},
  volume = {53},
  year = {2024},
}