Uncertainty principles for the Hankel-Gabor transform. (English) Zbl 1436.42011
Summary: In this paper, we prove an analogue of a time-frequency localization theorem for orthonormal sequences in \(L_{{\mu_\alpha}}^2(\mathbb{R}_+)\). As a consequence, we obtain an analogue of Shapiro’s umbrella theorem for the Hankel-Gabor transform \(V_g\). We also prove a mean dispersion inequality for \(V_g\). Finally, we get a strong version of the uncertainty inequality for orthonormal sequences of \(L_{{\mu_\alpha}}^2(\mathbb{R}_+)\).
MSC:
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 44A35 | Convolution as an integral transform |
| 42C05 | Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis |
Keywords:
uncertainty inequality; windowed Hankel transform; time-frequency localization theorem; mean dispersion inequalityReferences:
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