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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.06965 |
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Table of 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.