Wavelets on the 2-sphere and related manifolds

We present a group-theoretical derivation of the continuous wavelet transform (CWT) on the 2-sphere S2, based on the construction of coherent states associated to square integrable group representations. The parameter space X is the product of SO(3) × R*+, embedded into the Lorentz group SOo(3,1) via the Iwasawa decomposition, and X  -SOo(3,1)/. The space L2(S2,d) carries a unitary irreducible representation of SOo(3,1), which is square integrable over X, and thus yields the wavelets on S2 and the associated CWT.


Published in:
Reports on Mathematical Physics, 43, 1-2, 13-24
Year:
1999
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 Record created 2006-06-14, last modified 2018-12-03

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