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In mathematics and, in particular, functional analysis, convolution is a mathematical operation on two functions f and g, producing a third function that is typically viewed as a modified version of one of the original functions,giving the area overlap between the two functionsas a function of the amount that one of the original functions is translated.

Emphasis added.

It seems to me that since the two functions are being multiplied together and then integrated that the integral should give the

**product**of the areas of the two functions where the two functions overlap. My interpretation is significantly different than the rest of the world's, so I guess I'm wrong?