Non-harmonic Fourier Series and Exact Observability

Part of the Birkhäuser Advanced Texts / Basler Lehrbücher book series (BAT)


In this chapter we show how classical results on non-harmonic Fourier series imply exact observability for some systems governed by PDEs. The method of non-harmonic Fourier series for exact observability of PDEs is essentially limited to one space dimension or to rectangular domains in ℝn, since it uses that the eigenfunctions of the operator can be expressed (or approximated) by complex exponentials. We shall see that, in some of the above-mentioned cases, this method yields sharp estimates on the observability time and on the observation region.


Space Dimension Moment Problem Riesz Basis Rectangular Domain Regular Sequence 
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© Birkhäuser Verlag AG 2009

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