Time–Frequency Concentration, Heisenberg Type Uncertainty Principles and Localization Operators for the Continuous Dunkl Wavelet Transform on $$\mathbb {R}^{d}$$ R d

Time–Frequency Concentration, Heisenberg Type Uncertainty Principles and Localization Operators... We consider the continuous Dunkl wavelet transform $$\Phi ^{D}_{h} $$ Φ h D associated with the Dunkl operators on $$\mathbb {R}^{d}$$ R d . We analyze 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 $$\Phi ^{D}_{h} $$ Φ h D . Quantitative Shapiro’s dispersion uncertainty principle and umbrella theorem are proved for the Dunkl continuous wavelet transform. Finally, we investigate the localization operators for $$\Phi ^{D}_{h} $$ Φ h D , in particular we prove that they are in the Schatten-von Neumann class. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mediterranean Journal of Mathematics Springer Journals

Time–Frequency Concentration, Heisenberg Type Uncertainty Principles and Localization Operators for the Continuous Dunkl 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; Mathematics, general
ISSN
1660-5446
eISSN
1660-5454
D.O.I.
10.1007/s00009-017-0925-7
Publisher site
See Article on Publisher Site

Abstract

We consider the continuous Dunkl wavelet transform $$\Phi ^{D}_{h} $$ Φ h D associated with the Dunkl operators on $$\mathbb {R}^{d}$$ R d . We analyze 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 $$\Phi ^{D}_{h} $$ Φ h D . Quantitative Shapiro’s dispersion uncertainty principle and umbrella theorem are proved for the Dunkl continuous wavelet transform. Finally, we investigate the localization operators for $$\Phi ^{D}_{h} $$ Φ h D , in particular we prove that they are in the Schatten-von Neumann class.

Journal

Mediterranean Journal of MathematicsSpringer Journals

Published: Jun 8, 2017

References

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