On the properties of the anisotropic multivariate Hermite-Gauss functions

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Hacettepe Journal of Mathematics and Statistics
Volume:53 Issue:2
On the properties of the anisotropic multivariate Hermite-Gauss functions

On the properties of the anisotropic multivariate Hermite-Gauss functions

Authors : Shlomi Steinberg, Ömer Eğecioğlu, Lingqi Yan

Pages : 405-416

Doi:10.15672/hujms.1114405

View : 156 | Download : 121

Publication Date : 2024-04-23

Article Type : Research Paper

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 multivariate 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.
Keywords : Hermite functions, orthogonal basis, computational optics, linear canonical transform, Fourier transform, Wigner Vile distribution, eigenfunctions

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