# American Institute of Mathematical Sciences

November  2010, 14(4): 1487-1510. doi: 10.3934/dcdsb.2010.14.1487

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

 1 Politecnico di Torino, Dipartimento di Matematica, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

Received  June 2009 Revised  January 2010 Published  August 2010

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 systems. These sequences appear naturally when observability and controllability problems are reformulated in terms of suitable interpolation/moment problems.
The key contribution of the paper is to be found in the way used to prove that the two sequences are Riesz systems, an idea already applied to the study of different control problems.
Citation: Luciano Pandolfi. Riesz systems and moment method in the study of viscoelasticity in one space dimension. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1487-1510. doi: 10.3934/dcdsb.2010.14.1487
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