I am learning Fourier Analysis, and although things have been going well for a long time, soon they got extremely technical and I have started losing idea of why the proofs/theorems are important as I do not see many applications of these. So I would like to know good references for the following topics in Fourier analysis:
Paley Wiener theorems
Wiener Tauberian Theorem
Hilbert transform on $\mathbb R^n$
The first two have been discussed in Rudin. The proofs are long and very technical. Anyway, that should not be too much of a concern but I am not getting a feel for such theorems. Why are they important? What are their uses? Which references give decent exercises on these theorems?