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.

Thanks for your time.