Mean-dispersion principles and the Wigner transform
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866929327674753024 |
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| author | Boiti, Chiara Jornet, David Oliaro, Alessandro |
| author_facet | Boiti, Chiara Jornet, David Oliaro, Alessandro |
| contents | Given a function $f\in L^2(\mathbb R)$, we consider means and variances associated to $f$ and its Fourier transform $\hat{f}$, and explore their relations with the Wigner transform $W(f)$, obtaining a simple new proof of Shapiro's mean-dispersion principle. Uncertainty principles for orthonormal sequences in $L^2(\mathbb R)$ involving linear partial differential operators with polynomial coefficients and the Wigner distribution, or different Cohen class representations, are obtained, and an extension to the case of Riesz bases is studied. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2304_06965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mean-dispersion principles and the Wigner transform Boiti, Chiara Jornet, David Oliaro, Alessandro Analysis of PDEs Primary 42B10, 42C05, Secondary 33C45, 33C50 Given a function $f\in L^2(\mathbb R)$, we consider means and variances associated to $f$ and its Fourier transform $\hat{f}$, and explore their relations with the Wigner transform $W(f)$, obtaining a simple new proof of Shapiro's mean-dispersion principle. Uncertainty principles for orthonormal sequences in $L^2(\mathbb R)$ involving linear partial differential operators with polynomial coefficients and the Wigner distribution, or different Cohen class representations, are obtained, and an extension to the case of Riesz bases is studied. |
| title | Mean-dispersion principles and the Wigner transform |
| topic | Analysis of PDEs Primary 42B10, 42C05, Secondary 33C45, 33C50 |
| url | https://arxiv.org/abs/2304.06965 |