2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131108In this paper we provide some simple characterizations for the spherical harmonics coefficients of an isotropic random field on the sphere. The main result is a characterization of isotropic gaussian fields through independence of the coefficients of their development in spherical harmonics.9 pages. Submitted June 2005ProbabilityStatistics TheoryPrimary 60B15; secondary 62M15,62M40text