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$$L^p$$ quantitative uncertainty principles for the generalized Fourier transform associated with the spherical mean operator. (English) Zbl 1327.43005
In [Anal. Theory Appl. 29, No. 4, 309–332 (2013; Zbl 1313.42029)], the authors proved some uncertainty principles for the generalized Fourier transform associated with the spherical mean operator. In the paper under review, they prove some new $$L^p$$ quantitative uncertainty principles for the above transform. They extend Donoho-Stark’s uncertainty principle and then they study versions of the Heisenberg uncertainty principle.
##### MSC:
 43A32 Other transforms and operators of Fourier type 51F15 Reflection groups, reflection geometries
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