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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The authors are grateful to the referees for carefully reading the paper and for elaborate and valuable suggestions and comments.
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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
Keywords
- Gelfand pair
- spherical function
- spherical Fourier transform
- spherical Gabor transform
- uncertainty principles