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Mean-Dispersion Principles and the Wigner Transform.
- Source :
- Journal of Geometric Analysis; Jun2024, Vol. 34 Issue 6, p1-35, 35p
- Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10506926
- Volume :
- 34
- Issue :
- 6
- Database :
- Complementary Index
- Journal :
- Journal of Geometric Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 176471844
- Full Text :
- https://doi.org/10.1007/s12220-024-01601-0