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Exponential bases in Sobolev spaces in control and observation problems. (English) Zbl 0935.35014

Hoffmann, K.-H. (ed.) et al., Optimal control of partial differential equations. Proceedings of the IFIP WG 7.2 international conference, Chemnitz, Germany, April 20-25, 1998. Basel: Birkhäuser. ISNM, Int. Ser. Numer. Math. 133, 33-42 (1999).
Summary: The Fourier method in control systems reduces the study of controllability/observability to the study of related exponential families. In this paper we present examples of such systems, specifically those for which we can prove that the related exponential families form a Riesz basis in corresponding appropriately defined Sobolev spaces. This makes it possible to choose ‘natural’ pairs of spaces: the state space/observability space and the control space/state space, depending on whether an observation or a control problem is studied, respectively, so that the observation and control operators are isomorphisms.
For the entire collection see [Zbl 0921.00021].

MSC:

35B37 PDE in connection with control problems (MSC2000)
93B05 Controllability
35L20 Initial-boundary value problems for second-order hyperbolic equations
93B07 Observability
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