First we introduce a family of strongly harmonizing operators which smooth every suitably weighted continuous random field on an LCA group G into a strongly harmonizable one. Then, by means of these operators, we prove that the set of strongly harmonizable fields whose support is compact and...

Every continuous and bounded random field on k is the limit of a sequence of strongly harmonnizable random fields, uniformly on compact subsets of k. These harmonizable fields are obtained from the given random field by nonstationary linear filterings.