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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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Not a book but couldn't resist – Inquest Feb 12 '12 at 17:36
An excellent book is "Fourier analysis" by T.W. Körner. – Andrés E. Caicedo Feb 12 '12 at 17:37
@AndresCaicedo: Is that the same as Exercises in Fourier Analysis? – Ross Feb 12 '12 at 17:52
No, the book on Exercises is a companion to the main text. – Andrés E. Caicedo Feb 12 '12 at 18:29
"Fourier Analysis" by Stein and Shakarchi is a lovely book. It may look like it is aimed at a lower level (it is supposed to be an introductory text to analysis) but the material covered there is incredibly broad and wonderfully treated. – Chris Janjigian Feb 12 '12 at 18:43

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

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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

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