TITLE: Fourier Analysis textbook recommendation
QUESTION [13 upvotes]: I am taking a fourier analysis course at the graduate level and I am unhappy with the textbook (Stein and Shakarchi).  What I am looking for is a book that is less conversational and more to the point.  Further, I am not terribly interested in applications and would rather be exposed to how Fourier Analysis fits into the broader framework of analysis.  
For background, I used Baby Rudin for a one-year course in advanced calculus, I am currently taking a course from Kolmogorov and Fomin's Introductory Real Analysis and I have taken complex analysis (using Conway's text, Functions of One Complex Variable) as well as topology (using Munkres as well as Engelking) at the graduate level, but I have not yet been introduced to the Lebesgue integral.

REPLY [7 votes]: I can't help but recommend G. Folland's Tata notes on PDE, which are light, but not conversational/sloppy. It becomes immediately clear how Fourier transforms help.
Rudin's "Functional Analysis" treats Fourier transforms carefully, but gives the impression that he doesn't care about them very much. Not inspirational.
Hormander's volume I of his expanded PDE books is (unlike the later volumes) readable by everyone, and very useful.
The case of Fourier series in one variable is treated in a fashion meant to be down-to-earth, but also forward-looking, in my notes
 functions on circles, which includes discussion of Sobolev spaces and distributions on circles.