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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.2012-09-14

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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 side2012-09-14
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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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    @ool Then make sure to stay away from knives and such while reading Shakarchi and Stein.2012-09-14
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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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    @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.2012-09-14