Généralisation d'un théorème de Beurling et application à la théorie du contrôle
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文摘
Following some classical works of Paley and Wiener, Ingham and Beurling generalized Parseval's identity to nonharmonic Fourier series whose exponents are uniformly discrete. Motivated by control-theoretical problems, the last hypothesis was recently weakened in particular cases by Castro, Jaffard, Tucsnak and Zuazua. Generalizing another method, due to Kahane, we prove a general theorem containing all previous results. Its efficiency is illustrated by applications to control theory.