Riesz systems and moment method in the study of viscoelasticity in one space dimension

In this paper we study the equation of linear viscoelasticity and we prove that two sequences of functions, naturally associated with this equation, are Riesz sequences in $L^2(0,T$ for a suitable time $T$. It is to be noted that these functions solve suitable Volterra integro-differential equation, are not sequence of exponentials and are not eigenfunctions of operators naturally associated to the system. In spite of this, these sequences of functions appear naturally when observability and controllability problems are reformulated in terms of suitable interpolation/moment problems.