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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?

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nice responses. pls vote for your favourites! now i have too many books to choose from. –  ool Sep 14 '12 at 1:20

3 Answers 3

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.

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Dym and McKean always struck me as a little fast-paced and difficult for beginners. –  Jesse Madnick Sep 13 '12 at 6:27
    
If the OP needs to understand everything about Fourier analysis asap, I think a fast-paced book would be required. –  Per Manne Sep 13 '12 at 14:19
    
@Jesse It really depends on what you mean by "fast-paced",Jesse. Students with very strong calculus backgrounds(i.e.honors calculus a la Spivak and Hubbard/Hubbard) really shouldn't find Dym and McKean THAT difficult with some effort.More importantly,it gives a very comprehensive account that covers both the pure analytic and physical application aspects of the subject-which are both of equal importance.Most other introductions to the subject focus on one aspect or the other. –  Mathemagician1234 Sep 13 '12 at 19:19
    
can it be done in a week? with some calculus background –  ool Sep 14 '12 at 1:21
    
@col Uh-unless you just want to memorize formulas and give the trappings of theory, I don't know if that's really possible.Maybe for some genius who enters Harvard at age 15,but for most of us,no,I doubt it. –  Mathemagician1234 Sep 14 '12 at 1:44

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",

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i think my approach would be on the applied side –  ool Sep 14 '12 at 1:22

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.

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Someone told me Stein/Shakarchi make you want to stab yourself in the guts. : ) –  Matt N. Sep 13 '12 at 13:30
    
Yeah there where some passages... However, math tends generally to give that feeling, doesn't it? ;) –  AndreasS Sep 13 '12 at 18:00
    
It depends : ) (on who is teaching you and other factors, /mesuspects) –  Matt N. Sep 13 '12 at 23:03
    
well, this will only be me & the book, so... –  ool Sep 14 '12 at 1:21
    
@ool Then make sure to stay away from knives and such while reading Shakarchi and Stein. –  Matt N. Sep 14 '12 at 16:18

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