Need a crash course in fourier analysis, recommend resources

Question

I need to be able to understand everything about fourier analysis asap. Could you recommend one or two references or books that are considered 'the book' to learn this subject?

Answer 1

Dym and McKean's classic Fourier Series And Integrals. That's the book. You really need no other book on the subject-although you certainly might want to pursue it further.

Answer 2

It really depends on what level of Fourier analysis you're talking about, and whether you're coming at it from the applied (for example, how to use Fourier series or transforms in solving PDE's) or the pure real/harmonic/functional analysis sides. On the pure side, I'd recommend Edwards, "Fourier Series: A Modern Introduction" and Rudin, "Fourier Analysis on Groups",

Answer 3

Fourier Analysis: An Introduction by M. Stein and Rami Shakarchi is the book I'd recommend.

I used it to improve my knowledge of Fourier Analysis and I was quite satisfied with it. I think it covers the basic facts and also some rather special issues as for example Fourier Analysis on finite groups which is important in number theory.