TY - JOUR AU - MOKLYACHUK, M. P. AB - Random Oper. & Slocli. £)i(-J>)TM»(d«) J=0 >/S of a homogeneous isotropic on a sphere 5n random field £(.;", x), j G N, x G Sn, using observations of i » ® ) + *?(.?> x ) f°r J ^ , 6 Sn, where (> x) is a homogeneous isotropic on a sphere Sn random field uncorrelated with £(*,z), is considered. The least favourable spectral densities and the minimax (robust) spectral characteristics are determined for some classes of spectral densities. 1. Let Sn be the unit sphere in the n- dimensional Euclidean space, m n ( · ) be the Lebesgue measure on Sn, Slm(x), xeSn, m = 0,1,..., / = l,2,...,fc(m,n), be the orthonormal spherical harmonics of degree ra, /i(m, n) = (2m + n - 2)(m + n - 3)!((n - 2)!m!)~1 being the number of linearly independent spherical harmonics of degree m (for properties of spherical harmonics, see [1-3]). Let £(j, x) TI - A problem of minimax smoothing for homogeneous isotropic on a sphere random fields JF - Random Operators and Stochastic Equations DO - 10.1515/rose.1993.1.2.193 DA - 1993-01-01 UR - https://www.deepdyve.com/lp/de-gruyter/a-problem-of-minimax-smoothing-for-homogeneous-isotropic-on-a-sphere-EUmN7cA17c SP - 193 EP - 204 VL - 1 IS - 2 DP - DeepDyve ER -