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arXiv · 2012.13460

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

S. Dahlke·F. De Mari·E. De Vito·M. Hansen·M. Hasannasab·M. Quellmalz·G. Steidl·G. Teschke
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Abstract

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.

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S. Dahlke, F. De Mari, E. De Vito, M. Hansen, M. Hasannasab, M. Quellmalz, G. Steidl, G. Teschke. 2020-12-24. Continuous Wavelet Frames on the Sphere: The Group-Theoretic Approach Revisited. https://doi.org/10.1016/j.acha.2021.08.003

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