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Bounds on functions biorthogonal to sets of complex exponentials. Control of damped elastic systems. (English) Zbl 0742.93004

The paper is devoted to the problem of obtaining the explicit bounds on the norms of biorthogonal functions to sets of complex exponentials \(\exp(-\lambda_ kt)\), where \(\{\lambda_ k\}\) belong to a sector \(\{\lambda\in C: | \arg \lambda|\leq \theta\}\). The bounds obtained are uniform within a class of sequences which have some growth and separation properties. The main theorem leads to some results concerning the solvability of moment problems arising in control theory. As an application an exact null controllability result for a special system (a structurally damped Euler-Bernoulli plate) is proposed.

MSC:

93B05 Controllability
93C20 Control/observation systems governed by partial differential equations
93C05 Linear systems in control theory
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