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Benedicks–Amrein–Berthier type theorem related to Opdam–Cherednik transform

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Abstract

The aim of this paper is to prove a new uncertainty principle for the Opdam–Cherednik transform. This result is an analogue of a result Benedicks–Amrein–Berthier, it states that a non zero function f and its Opdam–Cherednik transform \(\mathcal {H}_{\alpha ,\beta }(f)\) cannot both have support of finite measure. We also prove Donoho–Strak’s local uncertainty principle to the Opdam–Cherednik transform.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their valuable comments.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Sciences Aïn Chock, University of Hassan II, 20100, Casablanca, Morocco

    Azzedine Achak & R. Daher

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  1. Azzedine Achak
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  2. R. Daher
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Correspondence to Azzedine Achak.

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Achak, A., Daher, R. Benedicks–Amrein–Berthier type theorem related to Opdam–Cherednik transform. J. Pseudo-Differ. Oper. Appl. 9, 431–441 (2018). https://doi.org/10.1007/s11868-017-0189-9

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  • DOI: https://doi.org/10.1007/s11868-017-0189-9

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