ABSTRACT
Similarly, let Dn be the class of all n-dimensional stationary isotropic covariances on IRn × IRn and D the class of all covariances which belong to Dn for all n 1.
By the same natural identification, one has
D . . . D n + 1 Dn Dn-1 and then
Since the representation (3) reduces to the form of the stationary case if and only if F(•, •) concentrates on the diagonal = ', it follows that
It is clear that the classes Gn are not empty. Swift [8] showed that as n increases, the covariance of a strongly har-
monizable isotropic random field becomes smoother. More specifically; the covariance has at least m = 1,2,... (n-1)
2 partial derivatives with respect to 1, 2 and . Here | • | is the greatest integer function, 1 = | |S | | , 2 = ||t||, and = arccos (s • t).
