On the positivity of Fourier transform of the stretched Gaußian function
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914720136560640 |
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| author | Liu, Hanwen |
| author_facet | Liu, Hanwen |
| contents | The stretched Gaußian function $f(\mathbf{x})=\exp \left(-\|\mathbf{x}\|^s\right)$, as a real function defined on $\mathbb{R}^d$, 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 $s \in(0,2]$, we prove that the Fourier transform of $f(\mathbf{x})=\exp \left(-\|\mathbf{x}\|^s\right)$ is everywhere positive on $\mathbb{R}^d$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_12843 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the positivity of Fourier transform of the stretched Gaußian function Liu, Hanwen Classical Analysis and ODEs The stretched Gaußian function $f(\mathbf{x})=\exp \left(-\|\mathbf{x}\|^s\right)$, as a real function defined on $\mathbb{R}^d$, 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 $s \in(0,2]$, we prove that the Fourier transform of $f(\mathbf{x})=\exp \left(-\|\mathbf{x}\|^s\right)$ is everywhere positive on $\mathbb{R}^d$. |
| title | On the positivity of Fourier transform of the stretched Gaußian function |
| topic | Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2403.12843 |