Operatorial non-stationary harmonizable processes

Operator theory proves to be a powerfull investigation tool in prediction theory helping to extend the multivariate case to the infinite-variate one. Taking the state space in the general context of an L(E)-module H, some conditions are obtained Sor the action df L(E) on H to find the best approximation of an element of H with respect to a submodule. For a harmonizable non-stationary process in a complete correlated action,using operator theory methods, a stationary investigation is given. Each harmonizable process has a spectrum obtained by its semispectral measure, and can be estimated by moving averages.