Avdonin, Sergei A.; Ivanov, Sergei A.; Russell, David L. 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]. Cited in 2 Documents MSC: 35B37 PDE in connection with control problems (MSC2000) 93B05 Controllability 35L20 Initial-boundary value problems for second-order hyperbolic equations 93B07 Observability Keywords:Fourier method; Riesz basis PDFBibTeX XMLCite \textit{S. A. Avdonin} et al., ISNM, Int. Ser. Numer. Math. 133, 33--42 (1999; Zbl 0935.35014)