Riesz systems and moment method in the study ofviscoelasticity  in one space dimension

Luciano Pandolfi

doi:10.3934/dcdsb.2010.14.1487

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2010, Volume 14, Issue 4: 1487-1510. Doi: 10.3934/dcdsb.2010.14.1487

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

Luciano Pandolfi^1,

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

Received: May 31, 2009

Revised: December 31, 2009

Published: May 2010

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Abstract

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.

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Mathematics Subject Classification: Primary: 47N70, 93C05; Secondary: 74D05.

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

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