  Functional data analysis in a mixed-effects model framework is done using
operator calculus. In this approach the functional parameters are treated as
serially correlated effects giving an alternative to the penalized likelihood
approach, where the functional parameters are treated as fixed effects.
Operator approximations for the necessary matrix computations are proposed, and
semi-explicit and numerically stable formulae of linear computational
complexity are derived for likelihood analysis. The operator approach renders
the usage of a functional basis unnecessary and clarifies the role of the
boundary conditions.
