Fundamental solution of the wave operator

Question

What is the explicit formula for a fundamental solution of the wave operator, where the space variable is in $\mathbb{R}^n$ with $n>1$? Thanks.

The operator I'm talking about is $$L=\partial_{tt}-\Delta_x$$ and for fundamental solution I mean a distribution $E$ (temperate) which satisfies $LE=\delta$ where $\delta$ is the Dirac distribution.

For $n=1$ one of such $E$ is $E(x,t)=(1/2)H(t)H(t^2-x^2)$ where $H$ is the Heaviside function.

I'm looking for expressions in higher dimensions.

Answer 1

What you are calling $E$ here, sounds like the Green's function of the wave operator....look at the bottom of the wiki page D'Alembert operator for the explicit form.

Answer 2

Higher dimensional cases will follow from Poisson's and Kirchhoff's formulas.