I am planning to study Fourier Analysis from a mathematical point of view. I know that there are some pre-requisites, such as, elements of Functional Analysis and Complex Analysis.
However, I would like to know what exactly I need to be familiar with before studying Fourier Analysis. I will be studying Fourier Analysis from Stein-Shakarchi.
I have done the whole of baby Rudin except Stieltjes Integrals (i.e. the last chapter).
I do not know anything about Complex Analysis or Functional Analysis.
Please tell me what I need to know on these two subjects because I have to make my base strong. I shall be consulting Rudin for Complex Analysis and Conway for Functional Analysis.