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Continuous wavelet frames on the sphere: The group-theoretic approach revisited
Applied and Computational Harmonic Analysis  (IF3.055),  Pub Date : 2021-08-17, DOI: 10.1016/j.acha.2021.08.003
S. Dahlke, F. De Mari, E. De Vito, M. Hansen, M. Hasannasab, M. Quellmalz, G. Steidl, G. Teschke

In [3], Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible 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 [3] by providing a complete and detailed proof.