On spectral representations of tensor random fields on the sphere

Abstract

We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square continuity, we derive their spectral decompositions in terms of generalized spherical functions. The properties of random coefficients of the decompositions are characterized, including such an important question as conditions of Gaussianity.

21 pages

References in corpus (5)

• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
• On the road to discovery of relic gravitational waves: The TE and BB Correlations in the cosmic microwave background radiation
• Decompositions of stochastic processes based on irreductible group representations
• Representations of SO(3) and angular polyspectra

Cited by in corpus (2)

• On Nonlinear Functionals of Random Spherical Eigenfunctions
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