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On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

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arxiv 2107.13188 v1 pith:7Q5DSLF5 submitted 2021-07-28 math-ph math.MP

On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions

classification math-ph math.MP
keywords functionshermite-gaussmultivariateopticspropertiesanisotropicapplicationsadmit
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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.

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