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...+1. The nth eigenspace Eλn = Hmn corresponds to the eigenvalue λn = n(n+m−1) and consists of traces of harmonic homogeneous of degree n polynomials on Sm. This case was considered in the papers [27], =-=[11]-=-, [39], [40], [24], [25], where u was subject either to the Gaussian distribution in Eλ or to the uniform one in S. Remark 1. Both distributions mentioned above are rotation invariant. Since hm−1 (Nu)...