I have to use InverseFourierSinTransForm in Mathematika for the function u[ω,t] but infortunately it does not work.It gives back the same! I tried it without the assumptions but it does not work again! Any help please?How can I write InverseFourierSinTransform to find the result? $$u(x,t)=\frac{2}{π}\int^{\infty}_{0}\hat{u}(\omega,t)sin(\omega x)d\omega$$
$$\hat{u}(\omega,t)= \sqrt{\frac{2}{π}}\frac{e^{-\omega^2 t}\omega}{\omega^2+a^2}$$
u[x_, t_] = InverseFourierSinTransform[v[ω, t], ω, x, Assumptions -> α > 0]
where $\hat{u} \to $ v[ω,t]
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