UNCERTAINTY OF POISSON WAVELETS

Poisson wavelets are a powerful tool in the analysis of spherical signals. In order to have a deeper characterization of them, we compute their uncertainty product, a quantity introduced for the first time by Narcowich and Ward [Nonstationary spherical wavelets for scattered data. Approximation Theory VIII, Vol. 2 (College Station, TX, 1995) (Ser. Approx. Decompos., 6). World Scientific Publishing, River Edge, NJ, 1995, pp. 301-308] and used to measure the trade-off between the space and frequency localization of a function. Surprisingly, the uncertainty product of Poisson wavelets tends to the minimal value in some limiting cases. This shows that in the case of spherical functions, it is not only the Gauss kernel that has this property.