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We consider the continuous wavelet transform $$\Phi _{h}^{W}$$ Φ h W associated with the Heckman–Opdam operators on $$\mathbb {R}^{d}$$ R d . We analyse the concentration of this transform on sets of finite measure. In particular, Donoho–Stark and Benedicks-type uncertainty principles are given. Next, we prove many versions of Heisenberg-type uncertainty principles for $$\Phi _{h}^{W}$$ Φ h W . Finally, we investigate the localization operators for $$\Phi _{h}^{W}$$ Φ h W , in particular we prove that they are in the Schatten–von Neumann class.
Journal of Pseudo-Differential Operators and Applications – Springer Journals
Published: Feb 28, 2017
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