Mixed needlets

The construction of needlet-type wavelets on sections of the spin line bundles over the sphere has been recently addressed in [D. Geller and D. Marinucci, J. Fourier Anal. Appl. 16 (2010), no. 6, 840–884; MR2737761; D. Geller et al., Phys. Rev. D 78 (2008), no. 12, 123533; D. Geller, X. Lan and D. Marinucci, Electron. J. Stat. 3 (2009), 1497–1530; MR2578835 (2011b:62250)]. Here we focus on an alternative proposal for needlets on this spin line bundle, in which needlet coefficients arise from the usual, rather than the spin, spherical harmonics, as in the previous constructions. We label this system mixed needlets and investigate in full their properties, including localization, the exact tight frame characterization, reconstruction formula, decomposition of functional spaces, and asymptotic uncorrelation in the stochastic case. We outline astrophysical applications.