Optimal designs for linear models with functional responses

In this work experimental designs with functional responses which are linearly dependent on some real control variables are studied. The goal is to determine an optimum design for a precise estimation of the unknown parameters. In other words, the values for the control variables are fixed in order to minimize (in some sense) the covariance matrix of the parameter estimators. It is assumed that processes belong to a Sobolev space, and the functional BLUE and the functional OLS estimator of the model parameter are computed in this space. The estimate in the $L^2$ space is then obtained as a more simple case.