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Distribution theory book

Two books I have been reading are Strichartz's A Guide to Distribution Theory and Fourier Transforms and PartII of Rudin's Functional Analysis . Both are good books.

However, the problem I am facing is that Rudin is sometimes too compact for me. It is like the author is trying to hide as much as insight and motivation as possible, which is not a very appropriate approach to distributions since they are actually a very 'practical' tool whose value lies in its usefulness. On the other extreme, Strichartz is too intuitive. For instance he does not give a clear examination about the topology of test functions, let alone the space of distributions ('At any rate, all functionals you will encounter are continuous' p4).

I found it difficult to combine these two books. It would be helpful if there is some good reference that lies between these two extremes.

Thanks!

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Hui Yu
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  • Don't forget that the topology of $\mathcal{D}(\Omega)$ is rather hard to define. Either you are satisfied with the notion of convergent sequence, or you must study topological vector spaces. – Siminore Sep 13 '12 at 14:03
  • (http://books.google.fr/books/about/Distributions_and_Operators.html?id=v7ydobPDBMgC&redir_esc=y)This is also a good reference. – Davide Giraudo Sep 13 '12 at 14:08
  • I closed this as a duplicate: there are at least 5 books in the linked thread beyond the two you mentioned in your question, the thread also links to http://mathoverflow.net/questions/20314/good-books-on-theory-of-distributions which has a staggering 19 answers. If somehow none of those suggested books are at the right level; please edit the question and also ping me to re-open the question. – Willie Wong Sep 13 '12 at 14:49
  • Note that Strichartz's book also has a section in the end on "Further readings". To give you a start on the many references in the links provided, maybe you want to start by check out Friedlander and Joshi, or perhaps Treves' Topological vector spaces, distributions, and kernels – Willie Wong Sep 13 '12 at 14:58

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