Continuous Gabor Transform for Strong Hypergroups
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We define a continuous Gabor transform for strong hypergroups and prove a Plancherel formula, an L 2 inversion formula and an uncertainty principle for it. As an example, we show how these techniques apply to the Bessel–Kingman hypergroups and to the dual Jacobi polynomial hypergroups. These examples have an interpretation in the setting of radial functions on R d and zonal functions on compact two-point homogeneous spaces, where they provide a new transform which possesses many properties of the classical Gabor transform.
KeywordsHomogeneous Space Uncertainty Principle Radial Function Inversion Formula Zonal Function
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