A Fourier transform of function R into function Q is defined as: $$Q(\underline{k}) = \int_{}^{}R(\underline{x}) e^{-i\underline{k}·\underline{x}} \mathrm{d}\underline{x}.$$ where I've underlined $\underline{x}$ and $\underline{k}$ to denote that they are a set of vectors.
Suppose that $R(\underline{x})$ is only a function of coordinate differences, for example, $R(\underline{x})=$($x$1-$x$2)($x$3-$x$1), where $\underline{x}$=($x$1,$x$2,$x$3).
Why must the Fourier transform $Q(\underline{k})$ contain a Dirac Delta function?
Note: The fact that the Fourier transform must contain a Dirac Delta function was mentioned on the bottom of page 25 of the following set of notes by my Physics professor, http://www-thphys.physics.ox.ac.uk/people/JohnCardy/qft/qftMT2012.pdf