Abstract
Controllability problems for N strings or beams controlled from a common endpoint are studied. We give necessary and sufficient conditions for simultaneous spectral and approximate controllability and describe the space of simultaneously reachable states as a function of the position of the endpoint. For each type of controllability result the sharp controllability time is obtained. The proofs are based on new results in nonharmonic Fourier series which describe Riesz bases of exponential divided differences.
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