A distributional version of Kirchhoffʹs formula

Kirchhoffʹs formula is the equivalent to Greenʹs Third Theorem for transient waves, representing the solution of the three-dimensional wave equation in terms of its boundary data. In this classical result two retarded layer potentials appear. We show in this paper a precise description of these potentials as time convolution with adequate tempered distributions with values on operator spaces. With these potentials in hands we give a self-contained proof of the formula with minimal smoothness requirements.