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| Auteurs principaux: | , , , , , , , |
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| Format: | Preprint |
| Publié: |
2020
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2012.13460 |
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- In \cite{AV99}, 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 \cite{AV99} by providing a complete and detailed proof.