Isotropic covariance matrix polynomials on spheres
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Ma, Chunsheng. Isotropic covariance matrix polynomials on spheres. Stochastic Analysis and Applications, vol. 34:no. 4:pp 679-706
This article characterizes the covariance matrix function of a Gaussian or elliptically contoured vector random field that is stationary, isotropic, and mean square continuous on the sphere. By applying the characterization to examine the validity of a matrix function whose entries are polynomials of degrees up to 4, we obtain a necessary and sufficient condition for the polynomial matrix to be an isotropic covariance matrix function on the sphere.
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