  A general formulation of the linear model with functional (random)
explanatory variable $X = X(t), t \in T$ , and scalar response Y is proposed.
It includes the standard functional linear model, based on the inner product in
the space $L^2[0,1]$, as a particular case. It also includes all models in
which Y is assumed to be (up to an additive noise) a linear combination of a
finite or countable collections of marginal variables X(t_j), with $t_j\in T$
or a linear combination of a finite number of linear projections of X. This
general formulation can be interpreted in terms of the RKHS space generated by
the covariance function of the process X(t). Some consistency results are
proved. A few experimental results are given in order to show the practical
interest of considering, in a unified framework, linear models based on a
finite number of marginals $X(t_j)$ of the process $X(t)$.
