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I have taken real analysis, but never learned Fourier analysis. What is a good book to get started? I'm not sure the Stein book would be good.

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    possible duplicate of [Fourier Analysis textbook recommendation](http://math.stackexchange.com/questions/4422/fourier-analysis-textbook-recommendation)2015-08-01

6 Answers 6

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"Fourier analysis" by T.W. Körner and its accompanied exercise book are the best.

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Gerald Folland's book (amazon) is excellent.

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Dym & McKean's book Fourier Series and Integrals has a better collection of applications than most (I suspect?) books do. Physics, number theory, probability, isoperimetric problems, ..... lots of stuff.

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A good place to start is Tolstov's little book on Fourier Analysis. It is published by Dover and it's inexpensive. There are nice problems.

Here is the Amazon page for it. The Stein books are wonderful but they do demand a serious level of skill with analysis. This book is a good place for you to start.

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I think that Folland's book deserves mention. Probably if you want to be thorough, you'll eventually read Dym McKean. Maybe Folland is easier at the start. Stein is not difficult, and it's very clear.

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please don't propose books that are impossible to find on internet, there are enough books and courses that are free to read on internet,

and the scientifics that you are should understand it is a huge social progress that everyone can FREELY access to the scientific knowledge.

look at any of the first links for :

google / fourier transform pdf

google / discrete fourier transform pdf

google / distribution fourier transform pdf

google / laplace transform pdf

google / filter convolution pdf

google / linear differential equation pdf

but be careful, it can take ~ 5 to 10 years to fully study the subject, it is so vast