Abstract
We reduce the problem of constructing an exponential Riesz basis in L 2 on the union of several intervals and the equivalent problem of constructing a sampling and interpolating set for the space of functions with limited multi-band spectra to a controllability problem for a model dynamical system. As a model we consider the wave equation with piecewise constant density and boundary control supported on the same union of intervals. For the case of two intervals we construct a controllable system and, as a consequence, a Riesz basis of exponentials produced by the spectrum of the system.
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Avdonin, S., Moran, W. (1999). Sampling and Interpolation of Functions with Multi-Band Spectra and Controllability Problems. In: Hoffmann, KH., Leugering, G., Tröltzsch, F., Caesar, S. (eds) Optimal Control of Partial Differential Equations. ISNM International Series of Numerical Mathematics, vol 133. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8691-8_4
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DOI: https://doi.org/10.1007/978-3-0348-8691-8_4
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