Wavelets on the 2-sphere and related manifolds

Antoine, Jean-Pierre;Vandergheynst, Pierre
(1999) Reports on Mathematical Physics — Vol. 43, n° 1-2, p. 13-24 (1999)

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  • Antoine, Jean-Pierreorcid-logoUCLouvain
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  • Vandergheynst, PierreUCLouvain
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Abstract
We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S-2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3)XR*+, embedded into the Lorentz group SOo(3, 1) via the Iwasawa decomposition, and X similar or equal to SOo(3, 1)/C. The space L-2(S2, d mu) carries a unitary irreducible representation of SOo(3, 1), which is square integrable over X, and thus yields the wavelets on S-2 and the associated CWT.
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Antoine, J.-P., & Vandergheynst, P. (1999). Wavelets on the 2-sphere and related manifolds. Reports on Mathematical Physics, 43(1-2), 13-24. https://doi.org/10.1016/S0034-4877(99)80011-1 (Original work published 1999)