Ingham-type inequalities for complex frequencies and applications to control theory

Abstract

AbstractFor complex valued sequences {ωn}n=1∞ of the form ωn=an+ibn with an∈R and bn⩾0, we prove inequalities of the form ∫0T|∑n=p∞xneitωn|2dt≈∑n=p∞|xn|2/(1+bn), for all sequences {xn} with ∑n=1∞|xn|2/(1+bn)<∞. We apply these to prove exact null-controllability for a class of hinged beam equations with mild internal damping with either boundary control or internal control