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Uncertainty principles for the multivariate continuous shearlet transform

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Abstract

In this paper, we present some new elements of harmonic analysis related to multivariate continuous shearlet transform introduced earlier in Dahlke et al. (J Fourier Anal Appl 16:340–364, 2010; The continuous shearlet transform in arbitrary space dimensions, Philipps-Universität Marburg, Marburg, 2008). Thus, some results (Parseval’s formula, inversion formula, etc.) are established. Next, we prove an analogue of Heisenberg’s inequality for shearlet transform. Last, we study shearlet transform on subset of finite measures.

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Authors and Affiliations

  1. Faculty of Sciences of Tunis, University of Tunis El Manar, 2092, Tunis, Tunisia

    Bochra Nefzi, Kamel Brahim & Ahmed Fitouhi

  2. Department of Mathematics, College of Science, University of Bisha, Bisha, Saudi Arabia

    Kamel Brahim

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  1. Bochra Nefzi
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  2. Kamel Brahim
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  3. Ahmed Fitouhi
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Correspondence to Bochra Nefzi.

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Nefzi, B., Brahim, K. & Fitouhi, A. Uncertainty principles for the multivariate continuous shearlet transform. J. Pseudo-Differ. Oper. Appl. 11, 517–542 (2020). https://doi.org/10.1007/s11868-019-00292-4

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