Sharp estimates for biorthogonal families to exponential functions associated to complex sequences without gap conditions
Résumé
The general goal of this work is to obtain upper and lower bounds for the L2-norm of biorthogonal families to complex exponential functions associated to sequences $\{ \Lambda_ k \}_{k \ge 1} \subset C$ which satisfy appropriate assumptions but without imposing a gap condition on the elements of the sequence. As a consequence, we also present new results on the cost of the boundary null controllability of parabolic systems at time $ T > 0 $. In this case, the eigenvalues of the generator of the $C_0$-semigroup associated to this parabolic system accumulate, do not satisfy a gap condition and can develop a positive minimal time for the null controllability.
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