Give three functions of two variables $a(x,y),b(x,y),c(x,y)$ one can construct the following convolution like integral:
$y(x,y) = \int dx' dy' a(x',y')b(x-x',y') c(x-x',y-y')$
which I have a hard time getting my head around.
Is there a name to that integral or can it be represented more elegantly in terms of some transformation (similar to the convolution theorem)? Specifically I'm interested in means to calculate it fast numerically.
Thanks.
PS: The generalization is of course: Given $n$ functions of $n-1$ variables... giving normal convolution for $n=2$