The Donoho–Stark, Benedicks and Heisenberg type uncertainty principles, and the localization operators for the Heckman–Opdam continuous wavelet transform on $${\mathbb {R}}^{d}$$ R d

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 transform on $${\mathbb {R}}^{d}$$ R d

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Publisher
Springer International Publishing
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
D.O.I.
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

References

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