On the positivity of Fourier transform of the stretched Gaußian function

2024/03/19 by Han‐Wen Liu, Liu, Hanwen
Engineering · #Advanced Electrical Measurement Techniques #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2403.12843

openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28

Abstract

The stretched Gaußian function f(x)=exp (-‖x‖^s), as a real function defined on ℝ^d, has found numerous applications in mathematics and physics. For instance, to describe results from spectroscopy or inelastic scattering, the Fourier transform of the stretched Gaußian function is needed. For s ∈(0,2], we prove that the Fourier transform of f(x)=exp (-‖x‖^s) is everywhere positive on ℝ^d.

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