Abstract
This work is motivated by the control problem for a linear elastic beam under a longitudinal load when the material of the beam has memory. We reduce the problem of controllability to a nonstandard moment problem. The solution of the latter problem is based on the Riesz basis property for a family of functions quadratically close to the nonharmonic exponentials. This result requires the detailed analysis of an integro--differential equation, and is of interest in itself for Function Theory.
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