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How to show that for $u \in L_{\mathbb{C}}^2$ and $a>0$,

$\int_0^a u(t) \sin{\sqrt{\lambda}t} \,dt = o(e^{|Im\sqrt{\lambda}|a}),\text{ as } |\lambda| \rightarrow \infty$

Note that $\lambda$ need not tend to infinity along the positive real axis.

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    First show that the result is true for $u(x)=e^{ikt\pi /a}$, then use density.2012-02-27

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