Strongly harmonizing operators and strongly harmonizable approximations of continuous random fields on LCA groups

Abstract

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 which admit a spectral stochastic density is dense in the set of continuous random fields on G endowed with the compact convergence topology T ( K ). Finally, new sequential approximation properties of such harmonizable fields are derived when T ( K ) is metrizable (e.g. G= R , R k or Z ).