We study the problem of finding conditions which guarantee that given operator data propagate under the control of unitary operators. This is a kind of moment problem and the way we solve it is based on unitary dilations. Comparing it with other results in this area, our approach has the advantages of
allowing the data to be unbounded operators,
considering arbitrary dilations, not necessarily regular ones.
The relationship between the moment problem and harmonizable multivariate discrete processes is indicated.
