"Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited,"Dahlke, StephanIn [1] Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissi- ble function by applying the unitary operators associated to a representation of the Lorentz group, which is square-integrable modulo the nilpotent factor of the Iwasawa decomposition. We prove necessary and sufficient conditions for functions on the sphere, which ensure that the corresponding system is a frame. We strengthen a similar result in [1] by providing a complete and detailed proof. [1] J.-P. Antoine and P. Vandergheynst. Wavelets on the 2-sphere: A group-theoretical approach. Appl. Comp. Harm. Anal., 7:262–291, 1999 |
« back