Need Self study book for Fourier Series and Generalized Functions

[jstrunk]

I need a book to self study Fourier Analysis that will also cover Generalized Functions, or at least prepare me to self study them.
I have Fourier Analysis and Its Applications by Folland and it isn't working for me.
The presentation very disorganized and unclear and no solution is provided for many of the exercises, so I can't verify my answers.
A book suitable for self study would have solutions for almost every exercise, preferably not just the bare solution, but how you get it.
Either that or bare solutions plus worked examples in the text.

I also have Schaum's Outline of Fourier Analysis. This has a lot of worked examples, so is OK as far as that goes, but it doesn't
cover Generalized Functions and I don't know if it provides sufficient background to study them.

 

[gleem]

For starters, you can try "Fourier Analysis and Generalised Functions" by M.J. Lighthill: a PDF copy is availalbe on line at https://www-dft.ts.infn.it/~rfantoni/teaching/Lighthill.pdf

 

[Baluncore]

I have no permitted access to that link, but the 1959 book is available from:
https://z-library.sk/book/121161122...urier-analysis-and-generalised-functions.html

 

[martinbn]

"A Guide to Distribution Theory and Fourier Transforms" - Robert S Strichartz

 

[jstrunk]

I also couldn't use the link to Lighthill but found it on the Internet Archive. There are only 18 official exercises in the whole book but from the comments on Amazon, it seems the proofs are kind of sketchy and filling in the blanks is almost like another set of exercises. And there are lots of examples. I think I will buy a copy rather that squint at it on the computer. As a funny side note, I noticed that the original price of the book was $1.95.
I will also check out the other recommendations.

 

[renormalize]

As a funny side note, I noticed that the original price of the book was $1.95.

Just $1.75 IN THE U.S.A. or 65p (13s) NET IN U.K. says the cover of the 1970 reprint that I bought in the late 1970s.

 

[MidgetDwarf]

Folland is a standard text. Do you find it hard to read do due to lack of mathematical maturity or weak analysis background?

By general functions, do you mean distribution theory?


Are you trying to approach this from a pure math perspective?

How good is your Lebesgue /Functional Analysis background?
Ie., how mucj do you know about operators.

 

[gleem]

I noticed that the original price of the book was $1.95.

That's what I paid for it.