Distribution for function

Question

I would like a good book to study distribution or generalized functions like the "Basic idea" of that Wiki page. Is there anyone could give me some good book references in this domain?

Thanks!

Answer 1

There are so many books on the theory of distributions. Probably it is also useful to use more than one. I see to put some order. To study the topology of the space of test functions and other, you can see in "A First Course in Sobolev Spaces" by G.Leoni, but also in "Functional Analysis" by W.Rudin (here you can find many results on topological vector spaces).

For the general theory, there are:

1. "Introduction to the Theory of Distributions" by F.G. Friedlander and M. Joshi.
2. "Functional Analysis" by W.Rudin

For tempered distributions (very important this space because you can define the Fourier transform of a distribution (tempered)), you can see:

3. "Pseudo-Differential Operators and Simmetries" by M. Ruzhansky
4. "Classical Fourier Analysis" by L. Grafakos
5. "Real Analysis Modern Techniques And Their Applications" by G. Folland

Also "Distributions Theory" by J.J. Duistermaat.

Good luck! (also I need)