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Spin wavelets on the sphere. (English) Zbl 1206.42039
The authors generalize existing approaches for wavelets on spheres to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In particular, they introduce needlet-type spin wavelets as an extension of the needlet approach recently introduced by Narcowich, Petrushev, and Ward, as well as Geller and Mayeli. The authors discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis of spin random fields. As the authors explain, the results are strongly motivated by cosmological applications, in particular in connection to the analysis of Cosmic Microwave Background polarization data.

MSC:
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
60G60 Random fields
33C55 Spherical harmonics
14C21 Pencils, nets, webs in algebraic geometry
83F05 Cosmology
58J05 Elliptic equations on manifolds, general theory
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