What is the Fourier transformation in the k-space?

Question

On wikipedia, we see the Fourier transformation examples in the case of the ordinary frequency and angular frequency scenario

https://en.wikipedia.org/wiki/Fourier_transform

But what is the transformation in the "k space" ? (with $k=2\pi/\lambda$) Is it given somewhere ?

Answer 1

It's the angular frequency case. Whether you want it to be unitary or not is your decision.

A physicist would write $e^{-i\omega t}$ or $e^{-kx}$ for the factors in the time and angular frequency case, and the space and space and angular wave number cases, respectively.

Answer 2

This is an example of physics. $k$ is the wave vector. Most problems are easier to solve in the "k space". Maybe take a look at https://en.wikipedia.org/wiki/Wave_vector