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The Donoho–Stark, Benedicks and Heisenberg type uncertainty principles, and the localization operators for the Heckman–Opdam continuous wavelet transf ...

The Donoho–Stark, Benedicks and Heisenberg type uncertainty principles, and the localization... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Pseudo-Differential Operators and Applications Springer Journals

The Donoho–Stark, Benedicks and Heisenberg type uncertainty principles, and the localization operators for the Heckman–Opdam continuous wavelet transf ...

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References (23)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Springer International Publishing
Subject
Mathematics; Analysis; Operator Theory; Partial Differential Equations; Functional Analysis; Applications of Mathematics; Algebra
ISSN
1662-9981
eISSN
1662-999X
DOI
10.1007/s11868-017-0194-z
Publisher site
See Article on Publisher Site

Abstract

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

Journal of Pseudo-Differential Operators and ApplicationsSpringer Journals

Published: Feb 28, 2017

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