Is it possible to multiply two (lighting) functions, converted to SH, by using only their SH coefficients?

All methods I have found so far - aside from multiplying the sampled result of the SH equations, and then converting it back to SH coefficients - seem to need one of the original functions, but all I will have is just two lists of coefficients.

What other ways are there to do this?

Sorry if this question is obvious, but calculus is not my best area, so I don't understand the formulas in a lot of explanations that well.

EDIT: don't know if it's standard procedure, but the result values of both functions (converted from SH back to a single value) are clamped to be at least 0.0, before they are multiplied together (one function is a mask for the other function).

[Edited by - Tree Penguin on September 23, 2010 11:00:02 AM]