Continuous spherical Gabor transform for Gelfand pair. (English) Zbl 1469.43002
A spherical Gabor transform is introduced which is based on the Gelfand pairs and their spherical Fourier transforms. Its fundamental properties, such as the Plancherel, Parseval and inversion formula, are established. A number of uncertainty principles (such as Donoho-Stark’s uncertainty principle, Lieb’s inequality and Beckner’s uncertainty principle) associated with this transformation are proved.
Reviewer: Elijah Liflyand (Ramat-Gan)
MSC:
| 43A30 | Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc. |
| 43A85 | Harmonic analysis on homogeneous spaces |
| 22E45 | Representations of Lie and linear algebraic groups over real fields: analytic methods |
| 43A32 | Other transforms and operators of Fourier type |
Keywords:
Gelfand pair; spherical function; spherical Fourier transform; spherical Gabor transform; uncertainty principleReferences:
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