Hey Johnny33.

Do you want to prove the convolution symbolically? If so, then there are a couple of ways to do this.

You could do it by starting from the original definition or you could use the relationship to the Fourier Transform since convolution already exists for that transform (i.e. use that as a gateway to proving the Hartley one).

Here is the relationship to the Fourier:

Hartley transform - Wikipedia, the free encyclopedia