TY  - JOUR
TI  - On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions
AU  - Shlomi Steinberg
AU  - Ömer Eğecioğlu
AU  - Ling-Qi Yan
PY  - 2024
T2  - Hacettepe Journal of Mathematics and Statistics
UR  - https://ssteinberg.xyz/2023/05/23/properties_of_AHG_functions/
DO  - 10.15672/hujms.1114405
VL  - 53
IS  - 2
SP  - 405
EP  - 416
AB  - 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.
KW  - hermite functions
KW  - orthogonal basis
KW  - computational optics
KW  - linear canonical transform
KW  - fourier transform
KW  - wigner-ville distribution
KW  - eigenfunctions
ER  -