Mathematical references that deal with Kirchhoff's integral theorem?

Question

I've seen Kirchhoff's integral theorem applied to the wave equation and similarly to the Helmholtz equation in optics books, but I am interested in gaining a mathematician's point of view on this topic.

Are there references that give fully rigorous proofs of the theorem? Does anyone have book references? Are there references that maybe touch upon generalizations?

Any info would be appreciated.

Answer 1

I learned the proof from Tikhonov's Equations of Mathematical Physics. But it is not an walk in the park.