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.
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.