On the Properties of the Anisotropic Multivariate Hermite-Gauss Functions
Shlomi Steinberg, \"Omer E\u{g}ecio\u{g}lu, Ling-Qi Yan
TL;DR
This paper explores the properties of anisotropic multivariate Hermite-Gauss functions, highlighting their potential applications in optics, signal analysis, and probability, and addressing a gap in existing literature.
Contribution
It provides a detailed analysis of anisotropic Hermite-Gauss functions, emphasizing their properties and potential uses in computational optics.
Findings
Characterization of anisotropic Hermite-Gauss functions
Potential applications in optics and signal analysis
Addresses a gap in the literature on multivariate Hermite-Gauss functions
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.
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