Spin Wavelets on the Sphere

Details Spin Wavelets on the Sphere Spin Wavelets on the Sphere

2008-11-18

arxiv.org/abs/0811.2935v3

Journal of Fourier Analysis and Applications, online first (2010)

Mathematics

Classical Analysis and ODEs

37 pages

Scientific paper

In recent years, a rapidly growing literature has focussed on the construction of wavelet systems to analyze functions defined on the sphere. Our purpose in this paper is to generalize these constructions to situations where sections of line bundles, rather than ordinary scalar-valued functions, are considered. In particular, we propose {\em needlet-type spin wavelets} as an extension of the needlet approach recently introduced by Narcowich, Petrushev and Ward, and then considered for more general manifolds by Geller and Mayeli. We discuss localization properties in the real and harmonic domains, and investigate stochastic properties for the analysis of spin random fields. Our results are strongly motivated by cosmological applications, in particular in connection to the analysis of Cosmic Microwave Background polarization data.

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