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In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approachto continuous wavelet frames on the sphere. The frame is constructed from asingle so-called admissible function by applying the unitary operatorsassociated to a representation of the Lorentz group, which is square-integrablemodulo the nilpotent factor of the Iwasawa decomposition. We prove necessaryand sufficient conditions for functions on the sphere, which ensure that thecorresponding system is a frame. We strengthen a similar result in \cite{AV99}by providing a complete and detailed proof.

Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited