Can anyone suggest a book on Fourier Analysis containing many good problems

Question

I am taking a basic course in Fourier Analysis in my undergrad Analysis class and I know the theory and related theorems. However, this is a relatively new zone for me and I would like a book that contains many good problems (solved/unsolved). I have been currently reading Rudin but its major problem is that there is practically no solved example.

What I want is a book/pdf that has many problems which will help strengthen my mathematical stronghold on the subject. Please note that I am not a physics student: I am essentially a pure maths student.

Thank you!!

Answer 1

You could try Analysis by Lieb and Loss, Chapter 5, its easier to read than most fourier analysis texts.

Rudin is pretty much a standard text though.

Answer 2

You can try Fourier Analysis by Stein and Shakarchi

Answer 3

If you're so proudly a pure mathematics student-which is self-defeatingly narrow in my opinion, but ok-you might want to bypass Fourier analysis in favor of the general subject of abstract harmonic analysis, for which Fourier analysis is a special case. The classic textbooks in this regard are Katznelson, Loomis and the more recent one by Folland. There's also the overview volume by Krantz and the books that take a real analysis perspective, such as Stein and Torchinsky.

Answer 4

I used Katznelson "An Introduction to Harmonic Analysis". It is a standard text on Fourier Series and Harmonic Analysis, with a set of good exercises after each section. It has been updated to cover even more topics since I used it 34 years ago.

Answer 5

I got this book: Fourier Series since it was really cheap. Haven't read through it yet, but it has great reviews.