> (...) then the correlation of f and g evaluated at x It really isn't the same, and oddly enough you unknowingly show that off, by mentioning that convolution

> (...) then the correlation of f and g evaluated at x It really isn't the same, and oddly enough you unknowingly show that off, by mentioning that convolution is the function that maps input functions to the output function, but the dot product is at best a single point evaluated with the output function.