## Wave equation fundamental solution.

uHi, I'm trying to solve the 1-dimensional wave equation:

$u_{xx}(x,t) - u_{tt}(x,t)=0$
$u(x,0)= f(x)$

I want my solution as a convolution product (with respect to x) of an hypothetical fundamental solution (I know heat and Laplace have one, so I tried to derive a solution for this) and $f(x)$. I want the solution to be finite.

I've found that :

$u(x,t) = f(x) *_{x} \mathcal{F}^{-1}(e^{\frac{-it}{\xi}})$

but I can't compute that inverse Fourier transform.