Quantitative uncertainty principles associated with the directional short-time Fourier transform. (English) Zbl 1489.43005
The authors discuss some basic harmonic analysis results related to the short-time Fourier transform, the Radon transform and short-time directional Fourier transform as well. Inspired by the inversion formula for the classical Fourier transform, they prove a new inversion formula for the short-time directional Fourier transform. Some general forms of \(L^p\)-Heisenberg’s uncertainty principle including a Nash-type inequality, a Clarkson-type inequality are established. Faris-Price uncertainty principles and local uncertainty principles for short-time directional Fourier transform are also proved.
Reviewer: Ashish Bansal (Delhi)
MSC:
| 43A32 | Other transforms and operators of Fourier type |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A15 | Special integral transforms (Legendre, Hilbert, etc.) |
| 35A23 | Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals |
| 44A12 | Radon transform |
Keywords:
directional short-time Fourier transform; directional radar ambiguity function; inversion theorem; Heisenberg’s type uncertainty principles; local uncertainty principlesReferences:
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