Titlebook: Distributed Systems with Persistent Memory; Control and Moment P Luciano Pandolfi Book 2014 The Author(s) 2014 Controllability via moment m

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Moment Problems and Exact Controllability,operties of the moment operator and of the Riesz sequences and to show the applications to exact controllability. In particular, the last worked example presents in a simplified setting the crucial ideas used in the study of controllability of systems with persistent memory.

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Book 2014tems, and applied mathematicians. Background of mathematics are the elements of functional?analysis, which is now standard among people working on distributed systems, and the author describes very clearly the instruments which are used at every step.

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2191-8112 ?analysis, which is now standard among people working on distributed systems, and the author describes very clearly the instruments which are used at every step.978-3-319-12246-5978-3-319-12247-2Series ISSN 2191-8112 Series E-ISSN 2191-8120

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An Example,tions, we study the very simple example of an unbounded viscoelastic string (laying on a half line) controlled at its end. We shall see in Chap.?2 that this example is simple but significant. Relying on known properties of the purely elastic string, we introduce the definition of the solutions and w

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The Model and Preliminaries,show the derivation of the heat equation with memory and the equation of viscoelasticity). In this chapter, we define and give formulas for the solutions of the system under study and we derive their properties, using an operator approach. We define the notion of controllability and prove the key re

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Controllability of the Wave Equation,n. For this reason, in this short chapter, we review the key results on the controllability of wave type equations. First, we describe a “hidden regularity” of the normal derivative of the solutions of the uncontrolled system and the observation inequality. A consequence is that the “active part” .