Consider the initial value problem for the wave equation on the whole number line:[br][center][math]u_{tt}\left(x,t\right)=a^2u_{xx}\left(x,t\right)[/math] with [math]x\in\mathbb{R},t>0[/math],[br][math]u\left(x,0\right)=f\left(x\right)[/math] with [math]x\in\mathbb{R}[/math],[br][math]u_t\left(x,0\right)=g\left(x\right)[/math] with [math]x\in\mathbb{R}[/math].[/center]