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Continuous Spherical Gabor Transform for Gelfand Pair

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Abstract

Using the basic properties of the Gelfand pairs and its spherical Fourier transform, we introduce the spherical Gabor transform. We show its fundamental properties, such as Plancherel, Parseval and inversion formula. Finally, we establish a number of uncertainty principles (such as Donoho–Stark’s uncertainty principle , Lieb inequality and Beckner’s uncertainty principle ) associated with this transformation.

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Acknowledgements

The authors are grateful to the referees for carefully reading the paper and for elaborate and valuable suggestions and comments.

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  1. Department of Mathematics, Faculty of Sciences, Equipe d’Analyse Harmonique et Probabilités, University Moulay Ismail, Zitoune, BP 11201 , Meknes, Morocco

    Moussa Faress & Saïd Fahlaoui

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  1. Moussa Faress
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  2. Saïd Fahlaoui
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Correspondence to Moussa Faress.

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Faress, M., Fahlaoui, S. Continuous Spherical Gabor Transform for Gelfand Pair. Mediterr. J. Math. 18, 83 (2021). https://doi.org/10.1007/s00009-021-01710-y

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  • DOI: https://doi.org/10.1007/s00009-021-01710-y

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