Bounds on functions biorthogonal to sets of complex exponentials. Control of damped elastic systems (Q1176310)

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.