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- Title
Mean-Dispersion Principles and the Wigner Transform.
- Authors
Boiti, Chiara; Jornet, David; Oliaro, Alessandro
- Abstract
Given a function f ∈ L 2 (R) , we consider means and variances associated to f and its Fourier transform f ^ , and explore their relations with the Wigner transform W(f), obtaining, as particular cases, a simple new proof of Shapiro's mean-dispersion principle, as well as a stronger result due to Jaming and Powell. Uncertainty principles for orthonormal sequences in L 2 (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.
- Subjects
PARTIAL differential operators; POLYNOMIAL operators; WIGNER distribution; HEISENBERG uncertainty principle; FOURIER transforms; DIFFERENTIAL operators
- Publication
Journal of Geometric Analysis, 2024, Vol 34, Issue 6, p1
- ISSN
1050-6926
- Publication type
Article
- DOI
10.1007/s12220-024-01601-0