Spin Wavelets on the Sphere

Understand

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.