Why is the transformed variable in some fourier transforms written as an index whereas sometimes it is written as an argument ? For example,
$$G_{\bf k}({\bf{v}},t)= \frac{1}{(2\pi)^3}\int g({\bf x},{\bf v},t)exp(-i{\bf k} . {\bf x})d{\bf x} $$
In the example above, why is $\bf k$ not written as a function argument but as an index ?