On the Takagi interpolation problem

Issues related to the existence and characterization of solutions of a generalization of the tangential Takagi interpolation problem are examined from the behavioral point of view. We associate to the interpolation data a “dualized” set of vector-exponential trajectories, which we model with the most powerful unfalsified model (MPUM). We show that there exists a representation of the MPUM for this set of trajectories which exhibits a special structure, and we study several properties of this representation, in particular those related to the signature of the Pick matrix of the data.