I'm currently working with Fourier transforms of measures on the $\mathbb{T}^n$ (more specifically in dimension two), i.e. $$ \hat{\mu}(k) = \int_{\mathbb{T}^n} e^{i k \cdot x} d\mu(x) $$ or something of that form. I am unfamiliar with this theory and would really appreciate a good reference on this topic.

Would anyone be able to point me to a good reference on the Fourier transform of measures over some unit cell? I have found literature for when $\mathbb{T}$ is replaced with $\mathbb{R}$, but am struggling to find a good reference for the requested case.

In case it is relevant, I am interested in the case when $k$ takes values on some lattice.

seriesrather than Fourier transform. $\endgroup$transformis used when working with measures. Thank you for the hint :) $\endgroup$