Moving Averages of Homogeneous Random Fields
Let X(g) be a homogeneous random field on a discrete locally compact Abelian group G. Let H(X) be the linear completion of {X(g): g E G} in L2 space. The following result is obtained: there exists a fundamental random field Y(g) on G with values in H(X) such that X(g) is obtained as a moving average of Y(g) if, and only if, X(g) has a spectral density which is positive almost everywhere with respect to the Haar measure on the dual group of G.