Is it possible to simplify the convolution integral if the functions are non-zero in disjoint areas? Possible Duplicate:
  When convolving two functions that are constants in a region and 0 everywhere else, where does the integration start?  




I have a function $f(x,y)$ and $h(x,y)$.  $f(x,y)$ has a value of $\frac{1}{3}$ when $x$ is between $\frac{1}{3}$ and $\frac{5}{9}$, and $y$ is between $0$ and $1$.  The function has a value of $0$ everywhere else.  Meanwhile, $h(x,y)$ has a value of 1 when both $x$ and $y$ are between $-\frac{1}{19}$ and $\frac{1}{19}$.

These two functions are non-zero in completely disjoint regions.  Is there a way to leverage this property to simplify the convolution integral?
Link to the closed-form solution:

wolframalpha



From left to right: $f$, $h$, and $f*h$: